Commons was substituted during the 1-1 draw with Hibernian at Easter Road after the midfielder pulled up with a hamstring problem.
The Hoops are already without suspended midfielder Scott Brown and Adam Matthews, who is recovering from shoulder surgery, while Mikael Lustig and fellow defender Emilio Izaguirre are both doubtful.
Speaking after the Leith encounter, Lennon attempted to be positive as he looks towards the Group H clash at Celtic Park.
"Kris knew straight away, he felt a pull," Lennon said. "We don't think it's a tear but if it's a strain it's at least a couple of weeks so it's not looking good for Tuesday.
"You can't tell how they are until they settle down but players more or less know straight away.
"It's a huge blow. He's been fantastic this season, he's at the top of his game, in great physical condition - you just don't see that one coming. He just stretched for a ball and felt something."
One player available to Lennon is James Forrest, who scored a wonderful goal to earn Celtic a share of the spoils.
"So we've got one going out and one coming in in James Forrest who's a brilliant player, and showed it again today," Lennon added.
"We'll have to assess the squad ahead of Tuesday. We're very hopeful Mika will be fit, Emilio should recover as well.
"We've obviously got a problem in midfield with Scott missing, and now Kris, so we'll see what we've got.
"I think we can beat Ajax at home but I don't know what personnel I'll have."