The 23-year-old was handed his first Premier League start of the season against the Cottagers and had a hand in two of his side's three goals.
But, after the winger was withdrawn with six minutes remaining, Wenger has admitted he has sustained a blow which will need to be assessed.
"Walcott has a glute muscle problem," the Frenchman told reporters.
"We nearly took him off at halftime, he nearly went down, but we left him on and on.
"In the end, it got worse and worse. At the moment, he is limping so I do not know whether he will be able to join the national team or not."
Walcott has been scoring freely so far this season, bagging seven goals so far, but is refusing to pen a new Gunners contract.