The Welshman limped off the pitch after coming on as a second-half substitute - lasting just nine minutes - and his French coach later revealed that the initial diagnosis "does not look good".
"It looks like another hamstring for Aaron Ramsey," the Gunners boss told reporters. "I don’t know how bad it is. Visually, when a player sits down and comes straight off, it does not look good.
"It’s a recurrence now of a few muscular injuries and it’s difficult to find out why."
Wenger rejected assertions that Ramsey was being overplayed, however, despite the midfielder featuring in 25 games in all competitions in 2014-15, and insisted that he has remained cautious with the 24-year-old due to his previous injury problems.
"I wanted to be cautious with him," he added. "I put him on because we were lacking some offensive power but it was not the greatest decision.
"Last year it was his thigh, this year it’s recurrence of hamstrings. This is his third of the year. He’s not been overplayed, Ramsey. Since he had these problems, I’m a bit more cautious with him."
Arsenal's win over Leicester moved them back into the top four, level on points with third-placed Southampton.