I have been wondering, can we Muslims keep silence for one or more day as a way of fasting? as it is in many traditions and religions to gain self-control and inner peace. I don't mean we do that instead of usual Ramadan fasts, but do it in any time that we feel it necessary or as an extra self-control way.
The fast of silence has no origin in Islam and Prophet Muhammad (saww) was never seen to do that. So keeping silence with the intention of fasting seems to be a kind of bidah and thus Haraam in Islam.
The following quote from Imam Ali ibn al-Husayn (as) can certify this claim:
صوم الصمت حرامٌ
Fast of silence is Haraam.
[Reference: Wasa'il al-Shiʿa, volume 7, page 390]
However, you are free to keep silence with any other intention. But based on this hadith from Prophet Muhammad (saww) it's better not to do it from day to night:
عن علي بن ابراهيم عن ابيه عن ابن ابي عمير عن منصور بن حازم عن ابي عبدالله جعفر بن محمد عليه السلام قال: قال رسول الله صلي الله عليه و آله: لا صمت یوماً إلی اللیل
Do not silence day to night.
You should also note that the verse 19:26 which states that Hazrat Maryam (as) had vowed the fast of silence to Allah, has nothing to do with Islamic sharia.
Fasting is an act of worship and the intention of worship is to please God and gain his nearness and consciousness. Had fasting of silence been a way to achieve that, Prophet Muhammad (PBUH) must have told us about this kind of worship. As there is no such thing reported from him, this is not a worship. Linking a label of "fast" is not appropriate for it.
There is no harm in doing such thing if it improves your self control. Just don't link it to religion.