The 23-year-old Wales international has not played since December 26 and is not expected to recover from his thigh injury until mid-March.
Ramsey had a superb start to the season scoring 13 goals by the end of November but even without him Arsenal have been top of the Premier League for most of the time since then.
"He will be out for four to six weeks," Wenger told reporters at his media briefing before this weekend's match against Crystal Palace.
"It is a blow for us because we have also lost Theo Walcott for a long period and Mathieu Flamini is suspended for four matches so before we had a lot of players in those positions but not now."
Arsenal were knocked off the top of the Premier League when they drew at Southampton on Tuesday and Manchester City won at Tottenham Hotspur on Wednesday.
They face improving Palace at the Emirates on Sunday.
(Reporting by Mike Collett; editing by Sudipto Ganguly)
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