The Spanish midfielder scored the Gunners opening goal in a 1-1 draw at Burnley on Wednesday night but was substituted two minutes before half-time and limped down the tunnel shaking his head.
Wenger confirmed that Fàbregas will definitely miss Saturday's Premier League match at home to Hull City and his involvement in the games against Aston Villa and Portsmouth at the end of the month is also looking doubtful.
But Wenger is optimistic the problem is "not long term''.
"Cesc had a scan today,'' said Wenger. "We have not had the result yet. The only thing that is sure is that he will not play on Saturday.
"Beyond that, it all depends on the scan. Is it a tightness that just presents a small risk on Saturday or is it a slight strain - grade one or two? We'll know that later.
"If it is a tear it is a small one and the maximum would be 10 days. So it is not long-term.''
Denilson could deputise for Fabregas against Hull after recovering from a back problem.
"Denilson is back and available for Saturday,'' Wenger said on Arsenal's official website.
Nicklas Bendtner, Tomas Rosicky, Gael Clichy and Armand Traore will be unavailable, and Wenger said: "The first back should be Traore, maybe for Aston Villa (on December 27).''