With Ozil, who also missed the 1-0 away win over Newcastle on December 29, and Ramsey sidelined with a shoulder and hamstring problem respectively, the Gunners will now be without Giroud after the Frenchman suffered a slight ankle problem in the match at St James' Park.
Wenger also confirmed that left-back Kieran Gibbs will miss the meeting with Cardiff, while Theo Walcott, Tomas Rosicky, Thomas Vermaelen and Jack Wilshere are all doubtful.
That could mean a key role for Lukas Podolski, who recently returned from long-term injury with a goal against West Ham on Boxing Day in a substitute appearance.
There has been much focus on Giroud this season, with the striker leading the line almost single-handedly for much of the campaign to date. Many pundits in the media have suggested that Arsenal need to sign another striker in the January transfer window, an assertion the player himself recently disputed.
As reported by Sky Sports, he told Canal+ this week:
If the coach wants me to rest, he can do it without buying a new striker.
Lukas Podolski is having a good comeback. Theo Walcott can play as a striker. We have the quality and the quantity.
I would rather not see a new striker come in.
Asked about those comments on Tuesday, Wenger said (per the Daily Mail):
Would you expect anything else? We have to give him credit. He has a fantastic combative attitude. We have a great confidence in him.
We are on alert in the market if something special turns up but we are not desperate.