Brown had just returned for Celtic in the 4-2 defeat to rivals Rangers, but his ankle problem surfaced again during the clash on Sunday.
“The ankle has gone again unfortunately,” bemoaned Lennon.
“He felt fine before the game, he trained the day before the match and looked great for an hour.
“He actually got us playing in the first half and was instrumental in both our goals so it was a blow losing him.
“We don’t know how long he is going to be out for now.
“It looks as if he is going to be shut down for a while until we can let it settle and get it right.”