The midfielder sustained a hamstring injury in Saturday's 1-1 Scottish Premiership draw against Hibernian and is not expected to feature against the Dutch side at Parkhead.
Commons has become a key player for the Scottish champion since his move from Derby County and if he is ruled out as expected, the 30-year-old's absence will be a major blow for manager Neil Lennon.
"Kris knew straight away, he felt a pull and signaled to us," Lennon said. "We don't think it's a tear, but if it is a strain it's a couple of weeks, so it's definitely not looking good for Tuesday. Losing Kris is a huge blow. He has been fantastic for us this season.
"He's at the top of his game and in great physical condition, so if he is out it will be a big loss."
Celtic is bottom of Group H after losing its first two games against AC Milan and Barcelona without scoring a goal, and Lennon knows the club can ill afford to slip up again.
"We can't lose it, put it that way," the former Northern Ireland midfielder said. "We are four points worse off in the group than we were at this stage last season. We have a bit of work to do.
"Home form is important to us, but Ajax are a very good side. Let's not beat about the bush. They will give us plenty to think about, plenty of problems. But we are at home and I think we will be confident enough to take the game to them."
As well as almost certainly being without Commons, the Glasgow outfit will be missing suspended captain Scott Brown following his red card against Barcelona.
Adam Matthews (shoulder) and former Ajax man Derk Boerrigter (ankle) are also ruled out, while there are doubts over Mikael Lustig (hip) and Emilio Izaguirre (illness).
Ajax will also be looking for its first win in the group after Mario Balotelli's last-gasp penalty denied the team victory in its last outing.
Stefano Denswil looked to have snatched a late win for Frank de Boer's side when he gave the team a 90th-minute lead, but Balotelli rescued a point for Milan when he converted a controversial spot kick with the last kick of the game.
De Boer's side comes into the Celtic game on the back of a 1-1 draw at FC Twente in the Eredivisie on Saturday. Niklas Moisander sat out that encounter but is expected to be fit to face the Bhoys.
Bojan (hamstring) is still out, however, while Lerin Duarte has not traveled to Scotland either.
Ajax, which is third in the Eredivisie table just as it is in Group H, was victorious 1-0 on its last visit to Parkhead back in August 2001, but has not won away from home this season.
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