Fabregas was taken off in Saturday's 1-1 draw with Sunderland after opening the scoring via a lucky deflection when Anton Ferdinand hit an attempted clearance off the midfielder's leg and back over his own goalkeeper.
Wenger revealed after the final whistle that Fabregas had sustained a hamstring injury and the player posted on his Twitter account: "Shame about the injury. I was feeling very good. Tomorrow [Monday] I'll know more about it. Have a good day."
However, Arsenal are not ready to detail the damage suffered by Fabregas before more comprehensive examinations take place.
"We don't know yet," Wenger told the club's official website. "It is difficult to say. He has a hamstring problem but I can't tell how long he will be out for. Any speculation would be wrong today because we have not had the scan."
After a summer in which he was the subject of sustained interest from Barcelona before being told to remain at Arsenal, Fabregas had reached top form recently, scoring three goals and claiming four assists in his past three games alone.
He is expected to miss Tuesday's Carling Cup game against rivals Tottenham but, in all likelihood, would not have played in any case given Wenger's tried and tested strategy of using the competition to field less experienced players.