The French Football Federation have given Giroud permission to leave the worldwide camp, as they prepare to face Germany in Cologne on Tuesday, and he has now returned back to England.
The 31-year-old, injured in Friday evening's 2-0 win over Wales in Paris, underwent tests in Rambouillet on Saturday and was shown to have suffered a right thigh strain, the French Football Federation confirmed on its website on Sunday.
"It's always a pleasure to play for the national team and I think we played a good game".
Giroud has scored twice in four Europa League starts, but his record of having netted at least 10 league goals in each of his seasons with Arsenal could be coming to an end.
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Giroud has featured in 17 games for Arsenal so far this season, scoring three times.
"I'm sure Arsene was watching, especially because Aaron [Ramsey] was playing too", said Giroud.
"I am not questioning myself about my future", said Giroud, as quoted by The Telegraph. "We will see what happens but I am happy at Arsenal for the moment". He's always supporting me and there is a lot of trust in each other, ' he said.
"I keep believing in my quality and I keep the faith". It's my 29th goal for France so I still have to score one more goal to reach Jean-Pierre Papin who was one of my favourite players.