The England international lasted just 36 minutes of the Gunners' 2-0 victory at St Mary's Stadium before being replaced by Hector Bellerin.
If he were to be ruled out, it would represent further disappointment in the competition for Oxlade-Chamberlain, who missed the 2014 triumph over Hull City through injury, while 12 months later he was only used as a late substitute against Aston Villa.
Providing an update on the player's status, Wenger said: "It's a hamstring problem but we don't know how bad it is.
"I don't know [about the FA Cup final]. He walks properly.
"I didn't see any incident where he had to stop a sprint. It was more fatigue, but it's difficult to assess now after the game.
"We will know maybe in the next 48 hours how bad it is."