Walcott twisted his left ankle in the turf after a tackle from Dean Whitehead and left the field on a stretcher.
“It is an ankle sprain – he is out of the next game for sure,” manager Arsene Wenger stated.
Wenger said captain Cesc Fabregas will be assessed on Thursday after suffering a hamstring injury in the first half.
The Gunners boss added: “Fabregas has a hamstring problem. We will assess that tomorrow. It is impossible to see how serious it is tonight. We will know tomorrow.
“It’s a concern that Cesc 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 for it to happen so early in the game but we have to face it and we did the job after that in a very professional way because we faced a Stoke team who defended very well, very compact.”
The Gunners will hope the 23-year-old has not suffered a serious problem, with Walcott’s injury already a blow as they push for trophies on four fronts.
Arsenal are one point behind Premier League leaders Manchester United in the title race having played one game more, could collect their first silverware in six years on Sunday, and play Leyton Orient in an FA Cup fifth-round replay on 1 March.
They also travel to Barcelona in the Champions League on 8 March carrying a 2-1 lead from the first leg.
And there can be little doubting that Arsenal would be a more formidable proposition in the Nou Camp with Walcott’s pace on the break.
The England winger was withdrawn on a stretcher midway through the second half of a hard-fought victory for the Gunners, with Sebastien Squillaci‘s eighth-minute header proving the difference between the sides.
Arsenal struggled to find their usual fluency and had to withstand considerable pressure from Stoke in the second half.
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We got the three points through focus, discipline and intelligence more than through flair tonight
Arsenal boss Arsene Wenger
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After the match, Wenger declared himself delighted with an uncharacteristic victory for substance over style.
“The game was massive for us and the three points were very important,” he said.
“We got them through focus, discipline and intelligence more than through flair tonight.
“Stoke are one of the most difficult teams to play against in this division. They can go anywhere and get a result and they defended very intelligently tonight.
“I couldn’t believe we scored with a header against Stoke but tonight we looked more dangerous from corners and set-pieces than from open play.”
The match took place almost exactly a year after Arsenal midfielder Aaron Ramsey broke his leg in a tackle by Stoke’s Ryan Shawcross.
But despite losing two players to injury against a team he had accused of playing “rugby” earlier in the season, Wenger said he was happy with the spirit in which the game was played.
Describing Whitehead’s challenge on Walcott as an “accident”, he said: “Overall it was a fair game – both sides were committed.”
As usual, one of Stoke’s principal threats came from the long throws of Rory Delap, with one delivery finding the head of Robert Huth, only for the German to nod wastefully over the bar.
In his post-match press conference, Wenger pondered whether the rules over throw-ins should be changed to cut down on teams hurling them into the box from long distance.
