Wenger rued his side's injury woes in midfield as Wilshere joined playmakers Aaron Ramsey (hamstring) and Mesut Ozil (knee) along with long-term absentee Santi Cazorla on the sidelines.
"I don't know if he'll be available on Sunday but it's definitely an ankle sprain," Wenger told reporters after the match.
"At the moment we have five big injuries and we're hoping to get some back. The earliest to come back is 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 Ozil on Sunday, but we could look a bit short."
German international Ozil, who is out of contract at the end of the season, has missed Arsenal's two cup games in January amid increasing speculation about his future at the Emirates.
Ramsey last played in Arsenal's league draw with Southampton on Dec. 10.
Arsenal, who are sixth in the table, travel to Bournemouth and host Crystal Palace in the league before the second leg of the League Cup semi-final on Jan. 24.
(Reporting by Aditi Prakash in Bengaluru)
