Edouard suffered an abductor muscle strain and the former Paris Saint Germain front man will be assessed over the next 24 hours.
The champions already have limited striking options with Scotland international Leigh Griffiths currently away from football for personal reasons.
Celtic manager Brendan Rodgers, who hopes to sign two new strikers in January, insists his squad can cope if Edouard, pictured, is ruled out of their remaining games this month against Dundee, Aberdeen and Rangers.
“Odsonne just felt a tightness around his abductor,” said Rodgers. “We’ll find out more in the next 24 hours. There’s not a great deal we can do.
“It’s been unfortunate for Odsonne because he’s had to play a lot more games than I’d have wanted because he’s been the only real striker available.
“But we have others who can fill in and we’ll always come up with a team we think can get a result.”
Mikey Johnston replaced Edouard last night and the 19-year-old scored his first goal for Celtic to add to earlier strikes from Anthony Ralston and Scott Sinclair. Winger Johnston would relish further opportunities to play through the middle. He said: “I don’t mind playing up front, I’ll play where I’m told. As long as I’m getting games I don’t mind. I’m just buzzing to get my first goal for Celtic.”
Motherwell stay nine points clear of the bottom of the table and manager Stephen Robinson says their games before the winter break against St Mirren, Kilmarnock and Hamilton will define their season.
“It was frustrating,” said Robinson. “Ultimately we were done by two individual errors for the first two goals. Their third goal was a super finish. We have three big games coming up which will dictate if we are looking up or down.”