Ramsey has been sidelined since scoring a hat-trick against Everton on February 3, and will miss both legs of the Gunners last 32 Europa League clash against Ostersunds.
Gunners coach Arsene Wenger said: “It is a little bit sensitive case because I expected him to be a bit further in his development of the groin problem.
“He doesn’t move forward as quickly as I expect it, and today I would say that certainly he will not be available even for the next game against Ostersund.
“Maybe for the cup final, I don’t know yet, it depends how he will progress from now.”
Meanwhile, Wenger called on Uefa to abolish the rule that renders Pierre-Emerick Aubameyang ineligible for Arsenal in the Europa League this season.
Aubameyang moved to north London for a club-record £56million last month, but cannot play in Europe as his former club Borussia Dortmund are also in the first knockout round after dropping down from the Champions League.
And Wenger said: “Unanimously, I believe that all the clubs agree now this rule has to disappear in Europe – especially because for example he played Dortmund, Dortmund has been reversed in the Europa League and he cannot play.”