Ryan Giggs's side will also be without Ethan Ampadu for the game at the Aviva Stadium on Tuesday as Wales aim to pick up their second win of their Nations League campaign having already beaten Ireland.
Gwion Edwards, Kieron Freeman and Swansea City winger Daniel James have all been called up as replacements for Giggs's depleted squad.
Ramsey's situation at club level has dominated the back pages in the build-up to the international break, with the midfielder looking increasingly likely to leave Arsenal next summer.
Indeed, the player himself, whose contract expires in 2019, has admitted that he expected to sign a new deal with the club, only for talks to have broken down.
Suggesting that he will leave the club on a free transfer, Ramsey told reporters: "Would I stay for the rest of the season? Of course, yeah. I am contracted to Arsenal and I am going to do my best now this season to try and achieve something special.
"Everything has been going great with the club – we thought we were in a position where we had agreed a deal but that’s no longer the case.
"So, I just have to carry on playing my football and do my best for Arsenal this season and I’ll leave the rest with the club now.
"Am I disappointed? That’s a decision that they have made and things happen in football and you just have to get on with it and carry on playing the best I can. That’s all I am concentrating on and giving my best for Arsenal."
Manchester United have been strongly linked with a move to sign Ramsey, while AC Milan have also been mooted as a potential interested party, with former Gunners chief executive Ivan Gazidis set to start his role with the club in the coming weeks.