The England winger was carried off during the 1-0 win over Stoke City on Wednesday and is definitely out of the League Cup final against Birmingham City on Sunday along with skipper Cesc Fabregas.
But while Fabregas has a good chance of being fit for the return at the Nou Camp on March 8 Wenger fears Walcott could also miss that game and the FA Cup replay against Leyton Orient next week.
“Walcott will be out for two to three weeks with an ankle problem,” Wenger told reporters.
“I would say it is very unlikely he will be fit for the second leg of the Barcelona game.
“I imagine the worst so maybe I will be surprised in a positive way but I just give you my gut feeling at the moment.”
Dutch striker Robin van Persie, who has missed the last two games through injury, will captain Arsenal on Sunday in the absence of Fabregas.
“I am delighted he is back,” Wenger said. “He is the vice-captain and will captain the side because the captain cannot play.”