The 26-year-old was forced off early into the second half of the contest after going down while blocking a Blues cross, although he was able to leave the pitch unaided.
Speaking to reporters after the final whistle, Wenger confirmed that Wilshere suffered a sprain and is now a doubt for the Gunners' trip to Bournemouth in the Premier League this weekend.
"I don't know if he'll be available on Sunday but it's definitely an ankle sprain," he said. "At the moment we have five big injuries and we're hoping to get some back. The earliest to come back is [Aaron] Ramsey and that is quite welcome because it's an area we're a bit short.
"If we didn't lose Jack tonight then we would have had Ramsey back and then maybe [Mesut] Ozil on Sunday, but we could look a bit short."
Wilshere, who has spent more than 1,000 days out injured in his senior career, has only just regained his place in the first team under Wenger after being shut out for the first few months of the campaign.