Walcott sprained his ankle in the 1-0 win over Stoke on Wednesday night and will miss definitely miss the game against Birmingham at Wembley.
Wenger also revealed that Fabregas suffered a hamstring injury and will be assessed by the club on Thursday.
Walcott was bundled over by Dean Whitehead on the edge of the box in the 68th minute, but referee Peter Walton waved play on.
The 21-year-old forward stayed on the ground, clearly in pain, before being carried off on a stretcher to be replaced by Denilson. Wenger described the injury as accidental afterwards and attributed no blame to Whitehead.
Fabregas had earlier lasted just 14 minutes before being replaced by Andrey Arshavin.
Wenger said: “Theo Walcott has an ankle sprain and he is out. For how long, I don’t know, but he is definitely out of Sunday.
“Fabregas has a hamstring problem. We will assess that tomorrow. It is impossible to see how serious it is tonight. We will know tomorrow.”
The Gunners boss added: “It is of course a concern that he (Fabregas) is injured but it happens unfortunately. He was very upset. I am as well. But it is not his fault or mine. It is part of sport.
“It’s strange when it happens early in the game but we have to face it. We did the job after that in a very professional way.”
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Double Injury Blow For Gunners