Giggs expects Ramsey to feature in the second leg with Milan on Thursday, but he will then treatment that has ruled him out of the China Cup.
"We've been in discussions with Arsenal and Aaron," Giggs told a media conference on Thursday.
"He's got a small procedure, it's the ideal time in the break to get it done. He'll be in the squad for AC Milan.
"It's a good time to get this done. It's a blow because he's a quality player but it's the best thing for the future for Aaron."
"You want your best players and Gareth is a tremendous player," added the manager. "He's someone who lights up the pitch whenever he's on it.
"You want your best players to travel. He's got a game just like most of the players at the weekend so we're constantly monitoring the players injury wise.
"There's been a few players who have picked up knocks this week so it's about constantly monitoring players and fingers crossed everyone's on the plane."
There is no place for Hal Robson-Kanu, though, with Giggs instead handing a first call-up to Preston North End forward Billy Bodin.
Danny Ward is not among the goalkeepers due to "administrative problems with the passport and his visa", while Ashley Williams will retain the captaincy.
Wales squad in full:
Goalkeepers: Michael Crowe (Ipswich Town), Wayne Hennessey (Crystal Palace), Chris Maxwell (Preston North End)
Defenders: Ethan Ampadu (Chelsea), James Chester (Aston Villa), Ben Davies (Tottenham), Chris Gunter (Reading), Declan John (Rangers), Tom Lockyer (Bristol Rovers), Christopher Mepham (Brentford), Connor Roberts (Swansea City), Neil Taylor (Aston Villa), Ashley Williams (Everton)