Giroud picked up an ankle problem in the win over Newcastle while Gibbs has a hamstring injury, which rules them both out of the Cardiff clash.
There are also concerns over Tomas Rosicky and Theo Walcott's fitness, the latter of whom was substituted late on at St James' Park and both are doubts.
Mesut Ozil and Aaron Ramsey are out until the middle of January with respective shoulder and thigh injuries and both missed the victory at Newcastle which saw the club return to the top of the Premier League.
Illness to both Thomas Vermaelen and Nacho Monreal means they are unlikely to feature and they join long-term injury victims Alex Oxlade-Chamberlain and Abou Diaby.
The absentees leave manager Arsene Wenger potentially without 10 first-team players for the visit of Cardiff as the Gunners look to get 2014 off to the best possible start.
Arsenal lead Manchester City by one point at the half-way point in the season however this injury crisis threatens to see their good work in the early months of the season unravel.
Such is the vast nature of Arsenal's injury crisis it might force Wenger into delving into the transfer market, not necessarily due to the seriousness of the blows which could see some players return for the FA Cup tie against Tottenham Hotspur, but the fragile nature of his squad.
Recent returnee Lukas Podolski is expected to lead the line while Nicklas Bendtner and Serge Gnabry are expected to be trusted with a role in the coming weeks.
Wenger will require unity from his Arsenal squad amid the difficult period and midfielder Mathieu Flamini says his side have the sufficient metal.
"In the past few years perhaps the physical side has been missing a bit," Flamini told the Daily Mirror. "What you need in any Arsenal side is the fighting spirit but you can see that we have it and that's great for us.
"If you want to win cups, sometimes you have to fight for it, especially in this league because it is the hardest league.
"We have a very good offensive team but it is so important to be strong defensively as that could make the difference at the end of the season.
"You have to come to places like here and typically be prepared to fight, then play your football and only by doing that can you win and get three points."