In the name of Allah
الحمدلله خلق الانسان علَّمه البیان نَزَّل القرآن بلسان عربیّ مبین، و الصلاة و السلام علی النبیّ العربیّ سیّد ولد آدم و خاتم الانبیاء و المرسلین
As far as I searched, there is no tradition to point that it is considered as a Wajib (mandatory) act for Muslim, but there are some items which make us learning Arabic. For instance by learning Arabic, perhaps we can comprehend the Quran better which is in Arabic, or in reading the origin Ahadith and so on.
On the other hand, Arabic language is counted as one of the most populous language and according to my research, Arabic is considered as the Sixth language of the world (from the aspect of the population).
There is a tradition from Imam Ali (peace be upon him) that said:
« تَعـَلـَّموا العَرَبیّــﮥ و عَـلِّـموها النّاسَ . Learn Arabic and
teach it to the people.
Or Imam Sadiq (a.s.) said:
تَـعَـلَّـموا العَرَبیّــﮥَ فَـإنَّـها کلامُ اللهِ الَّـذی
یُـکَـلِّـمُ بِـهِ خَـلْـقَـهُ .
Learn Arabic, because this is the speech of the God who speaks to his
creatures.
Even Imam Khomeini has illustrate concerning the significance of learning Arabic:
Do not say that Arabic is not from us, Arabic language is from us,
Arabic language is the language of Islam and Islam is for all people.
It could be considered from other aspects such as:
Being able to speak with Arab Muslims in interchanging the Islamic
knowledge and civilizations and so forth.
Being able to have discussion with other Muslims (Arabs) regarding
Islamic issues such as Quran, hadiths and so forth.
Being able to watching other Islamic Arabic channels of TV and radio
and obtaining Islamic and scientific revenue by watching and hearing
them.
Finally it could be a more unity between Muslims in different
languages.
Reference(s):