Giroud picked up a thigh injury during his 73-minute long run-out in the 2-0 win against Wales on Friday [10 November] and has returned to his club for further treatment after scans revealed the blow, according to the French Football Federation.
The 31-year-old netted the second goal in the friendly win over Chris Coleman's men but will be unavailable for his country when they face the world champions in Cologne on Tuesday [14 November].
The news comes at the worst possible time for Gunners manager Arsene Wenger, ahead of the daunting visit of rivals Tottenham, who could now be without one of his most trusted performers when Spurs travel to The Emirates Stadium next Saturday [18 November].
Having not started any of Arsenal's 11 Premier League games this season, Giroud would likely have been named among the substitutes for the game against Mauricio Pochettino's side. In 10 previous appearances against Tottenham he has scored two goals and made one assist but has appeared on the winning side on four occasions.
The former Montpellier forward was close to joining Everton during the summer transfer window but stayed to play a leading role in the clubs domestic cup and European campaigns.
"I am not questioning myself about my future," said Giroud, as quoted by The Telegraph after the friendly in Paris. "I am happy at Arsenal and I am fine with the decision to stay because I want to. I am thinking that the story between the club and myself is not over and not finished. We will see what happens but I am happy at Arsenal for the moment.
"Arsene's always supporting me and there is a lot of trust in each other. He trusts in me and I try to give it back on the pitch when I can."
Wenger currently has to contend with five players on the Arsenal injury list including David Ospina, Shkodran Mustafi, Calum Chambers, Danny Welbeck and Santi Cazorla; though it remains to be seen whether any other injuries will surface from the second round of international matches.
If Giroud is ruled out of the Tottenham clash then Wenger could call on 18-year-old Eddie Nketiah, who has recently emerged as the latest Arsenal success story to emerge from their academy.
The Lewisham-born forward netted his first Arsenal goals in the Carabao Cup win over Norwich City and Wenger admitted he could soon be in line for a Premier League debut.
And Nketieh provided another timely reminder to Wenger of his ability by scoring the winning goal in the England Under-19s' 2-1 win over Iceland in Bulgaria on Saturday [11 November]. The solitary strike follows the teenager scoring four times in the 6-0 win over Faroe Islands.