The Wales midfielder lasted just 20 minutes of the Premier League clash at The Emirates before pulling up with the problem in the first half.
Wenger has now confirmed that Ramsey is set to be out of action for around three weeks with the injury.
The Arsenal boss also revealed the latest Arsenal team news concerning Olivier Giroud, Danny Welbeck and Alex Oxlade-Chamberlain.
Speaking at his pre-match news conference, Wenger replied when asked how long Ramsey will be out for: “I would say 21 days.”
He continued: “Overall from the other night I think we lose Ramsey, and Giroud has a test. Giroud should be alright.
“Maybe Welbeck will come back into the group and that’s basically it. Chamberlain has a test today [Friday] as well but I think he will be alright.”
Arsenal are currently gearing up for their crunch Premier League clash against Chelsea at Stamford Bridge on Saturday afternoon as they look to bounce back from their surprise loss to Watford.
The Gunners are nine points behind leaders Chelsea as they look for a victory to get their Premier League title bid back on track.
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