Wa alaikum assalaam
No, it is not an innovation as there are some hadeeth a recommending the fast the first half of it but scholars say that this is if a person was going to be weak to Fast Ramadan.

The Prophet salla Allahu alaihi wa sallam used to fast most of Shaaban.

Assalamu alaykum, I understand that the Prophet use to fast most in Sha’ban but i want to know if he (saw) use to fast the first two weeks of Sha’ban. Some people fast the first 2 weeks or it’s an innovation?

Fasting |