President Muhammadu Buhari was represented at the funeral by his Chief of Staff, Abba Kyari.
Abu-Ali and some of his men were killed by Boko Haram insurgents in a night raid at Mallam Fatori, Borno state, last Friday.
Six soldiers - Muazu Ibrahim, Hussani Jafaru, Bassey Okon, Chukwu Simon and Patrick Paul - were killed alongside the Abu-Ali in the attack.
At the brief funeral held at the National Cemetery, Buratai extolled the bravery and gallantry of Abu-Ali and his men.
Abu-Ali led the operation to recapture Baga as well as other successful onslaughts against the terrorists.