The former Manchester United forward came off in the 73rd minute of the encounter at Stamford Bridge following a collision with Blues defender David Luiz.
Speaking after the game, Wenger confirmed that Welbeck had suffered "a groin problem" and will now face a medical assessment.
"I don't know how severe it is," he told the Evening Standard. "It looks like it is a 'good' groin problem. Not an easy one."
Welbeck has featured in all five of Arsenal's Premier League games so far this season, contributing three goals.