According to Sheik and Islamic Scholar Imran Hossein, fiat currency is indeed haram. In his Merchants of Venice Youtube video, the sheik succesfully builds the case for including fiat currency under the umbrella of riba, a system of zulm (oppression) (timestamp 12:56).
Gold and Silver as money or items of value to be used in exchange are mentioned several times in the Quran as described in this source.
Fair in the eyes of men is the love of things they covet: Women and sons; Heaped-up hoards of gold and silver; horses branded (for blood and excellence); and (wealth of) cattle and well-tilled land. Such are the possessions of this world's life; but in nearness to God is the best of the goals (To return to). زُيِّنَ لِلنَّاسِ حُبُّ الشَّهَوَاتِ مِنَ النِسَاء وَالْبَنِينَ وَالْقَنَاطِيرِ الْمُقَنْطَرَةِ مِنَ الذَّهَبِ وَالْفِضَّةِ وَالْخَيْلِ الْمُسَوَّمَةِ وَالأَنعَامِ وَالْحَرْثِ ۗ ذَلِكَ مَتَاعُ الْحَيَاةِ الدُّنْيَا ۖ وَاللَّهُ عِنْدَهُ حُسْنُ الْمَآبِ
Among the People of the Book are some who, if entrusted with a hoard of gold, will (readily) pay it back; others, who, if entrusted with a single silver coin, will not repay it unless thou constantly stoodest demanding, because, they say, "there is no call on us (to keep faith) with these ignorant (Pagans)." but they tell a lie against God, and (well) they know it. وَمِنْ أَهْلِ الْكِتَابِ مَنْ إِنْ تَأْمَنْهُ بِقِنطَارٍ يُؤَدِّهِ إِلَيْكَ وَمِنْهُمْ مَنْ إِنْ تَأْمَنْهُ بِدِينَارٍ لاَ يُؤَدِّهِ إِلَيْكَ إِلاَّ مَا دُمْتَ عَلَيْهِ قَائِماً ۗ ذَلِكَ بِأَنَّهُمْ قَالُوا لَيْسَ عَلَيْنَا فِي الأُمِّيِّينَ سَبِيلٌ وَيَقُولُونَ عَلَى اللَّهِ الْكَذِبَ وَهُمْ يَعْلَمُونَ
Wa Sharawhu Bithamanin Bakhsin Darāhima Ma`dūdatin Wa Kānū Fīhi Mina Az-Zāhidīna (Yūsuf: 20). 012.020 The (Brethren) sold him for a miserable price, for a few dirhams counted out: in such low estimation did they hold him! وَشَرَوْهُ بِثَمَنٍ بَخْسٍ دَرَاهِمَ مَعْدُودَةٍ وَكَانُوا فِيهِ مِنَ الزَّاهِدِينَ
Inna Al-Ladhīna Kafarū Wa Mātū Wa Hum Kuffārun Falan Yuqbala Min 'Aĥadihim Mil'u Al-'Arđi Dhahabāan Wa Law Aftadá Bihi ۗ 'Ūlā'ika Lahum
Adhābun 'Alīmun Wa Mā Lahum Min Nāşirīna ('āli Imrān: 91).
As to those who reject Faith, and die rejecting,- never would be accepted from any such as much gold as the earth contains, though they should offer it for ransom. For such is (in store) a penalty grievous, and they will find no helpers. إِنَّ الَّذِينَ كَفَرُوا وَمَاتُوا وَهُمْ كُفَّارٌ فَلَنْ يُقْبَلَ مِنْ أَحَدِهِمْ مِلْءُ الأَرْضِ ذَهَباً وَلَوْ افْتَدَى بِهِ ۗ أُوْلَائِكَ لَهُمْ عَذَابٌ أَلِيمٌ وَمَا لَهُمْ مِنْ نَاصِرِينَ
“O ye who believe! Lo! many of the (Jewish) rabbis and the (Christian) monks devour the wealth of mankind wantonly(in a deliberate and unprovoked manner) and debar (men) from the way of Allah. They who hoard up gold and silver and spend it not (this would obviously be in the context of use of gold and silver as money) in the way of Allah, unto them give tidings (O Muhammad) of a painful doom.” (Qur’ān, al-Tauba, 9:34)
“And if you wish to have (one) wife in place of another and you have given one of them a Qintār (i.e., a treasure of gold and silver coins), then take not from it anything; would you take it by slandering (her) and (doing her) manifest wrong?” (Qur’ān, al-Nisā, 4:20)
In many verses; 18:31, 22:23, 35:33, 43:53, 43:71, and 76:21; "the Qur’ān goes on to reveal the extraordinary news that gold and silver would maintain their status as things of great value in the next world as well. In other words, gold and silver possess a spiritual reality as things of value, in addition to their value in this material world" (quranlifesite).
All the above are also supported by many hadiths which are also quoted in the quranlifesite web site.
With the importance of gold and silver as hard currency firmly established, sheik Imran Hosein and other Islamic sources also make it reasonably clear that other physical commodities can be substituted for gold and silver as long as these substitutions have intrinsic value and can maintain their intrinsic value for lengthy periods of time.
"Allah's messenger said that when you have a shortage of dinar and dirham in the market you can turn to other things as money on the condition that they have intrinsic value. So in Medina they used dates as money" (Hosein ts47:23).
"If a transaction involves an exchange of gold for gold, or silver for silver, or wheat for wheat, or barley for barley, or dates for dates, or of salt for salt; it must be equal, both sides must be equal in quantity. If you have two kilograms on this side you must have two kilograms on the other side.
It must be equal for equal, and it must be hand to hand. Therefore a credit transaction is prohibited. What is common to all six; gold, silver, wheat, barley, dates, and salt is that they were all used as money" (Hosein ts51:02).
"When there was a shortage of gold and silver in the market they (the Muslims) would turn to commodities of food consumption which had a shelf life and which were in abundant supply in the market and which like gold and silver had intrinsic value. The value of the money was inside the money. It was not a fictitious value." (hosein ts53:36)
In contrast, fiat currency, and in particular paper money or electronic money has no intrinsic value. Any value assigned to it by governing authorities are fictitious values.
Therefore, even before getting into the riba built into the fiat monetary system, the fact that the fiat currency has no intrinsic value within itself makes it instrinsicly fraudulent.
When currency is true currency with the value intrinsic to the currency, the currency cannot be inflated or deflated. Inflation is a form of riba. Sh. Imran Hosein details the example of the inflation of the Pakistani Rupee from 1.75rupees/US$ in 1964 to 110rupees/US$ in 2020 (Hosein ts59:57). One needs to keep in mind that the US dollar, itself a fiat currency, also devalued against gold, silver, or other real physical assets.
"As long as money had intrinsic value we never had inflation."(Hosein ts55:32)
"As soon as they remove real money from the market and replace it with bogus fraudulent and haram money, we now have inflation." (Hosein ts55:58)
"Number one, they are creating money out of thin air, that's the first haram so you're a god now. You can create wealth out of thin air." (Hosein ts56:13)
"you take a piece of paper and you print a picture on it and you put a number on it and you assign a fictitious value to it and it becomes money?
and because you control power in the world, you are the oppressor." (Hosein 56:24)
"Not only did they replace gold and silver in the market with their own paper money, but they did something more, they prohibited the use of gold and silver as money.
Just there, in the articles of agreement of the international monetary fund. The reason why they did that is because once gold and silver comes into the market, the paper will be gone, finished, cannot survive.
So in order for their bogus system of oppression and exploitation to be successful, they had to ban the use of gold and silver as money and they did it." (Hosein ts58:53)
Thus the whole world's monetary system is based on riba and the use of gold and silver for currency is prohibited. As inflation of the fiat currency continues there continues to be an enormous transfer of wealth from the masses of the people to a predatory elite few.
"When an economy is based on riba, wealth will no longer circulate through the economy. The rich will now remain permanently rich and the poor will remain permanently poor." (Hosein ts 30:30)