Is it permissible for a Muslim to fast from speaking for one or more days, like the fasting of the Prophet Zachariah?

A Muslim is not permitted to worship Allah except in the manner prescribed by the Messenger of Allah, peace and blessings be upon him. Seeking closeness to Allah through silence is not among the acts prescribed by the Prophet, peace and blessings be upon him. In the Hadith, the Prophet, peace and blessings be upon him, said concerning Abu Isra'il, who vowed to stand, not sit, not seek shade, not speak, and to fast: "Let him speak, and let him seek shade, and let him sit, and let him complete his fast."

This is if the silence is intended as an act of worship to Allah. However, if refraining from speech is in compliance with the Messenger's command, peace and blessings be upon him, in the Hadith: "Whoever believes in Allah and the Last Day should speak good or remain silent," then that is a great act of worship.

The fasting of Zakariya, peace be upon him, from speech was not an act of worship, but rather a sign that Allah made for him, and proof of his wife's pregnancy. Allah Almighty said: (He said, "My Lord, make for me a sign." He said, "Your sign is that you will not speak to the people for three nights, except by gesture.")