All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
It is not obligatory to fast the month of Muharram or any day of it. Scholars had different opinions regarding fasting the tenth day of Muharram; was it obligatory before the obligation of fasting Ramadan or not? There are two opinions regarding this issue; however, after the obligation of fasting Ramadan, fasting the tenth day of Muharram became favorable. Imaam Ash-Shawkaani said, “Ibn ‘Abdul-Barr reported the consensus of the scholars regarding the non- obligation of fasting the tenth of Muharram and the fact that it is favorable to fast it. ”
One of the proofs that it is recommended to fast voluntarily in Muharram is that the Prophet said: “The best fasting after Ramadan is the fasting of Muharram and the best prayer after the obligatory prayer is the night voluntary prayer.” [Muslim, Abu Daawood, An-Nasaa’i, Ibn Maajah and At-Tirmithi]
It is favorable to fast the tenth of Muharram along with the ninth or to fast the tenth of Muharram along with one day before it and one day after it, or to fast it along with a day before it or a day after it to be different from the Jews. It is also sufficient to fast the tenth of Muharram alone.
Allah knows best.