The France international returned late to pre-season training due to featuring for his country at the World Cup in Brazil.
Giroud played the first half of Arsenal's 1-0 defeat to Ligue 1 runners-up Monaco in the Emirates Cup and appeared to be lacking in fitness.
But Wenger - who sees his side contest the Community Shield with Manchester City on Sunday - is not concerned by the 27-year-old's display.
"He had only three weeks rest, it was not an eternity and he had to come back quickly," Wenger said.
"But sometimes when you come back late you want to work hard and in a game you are not as sharp.
"He's not put weight on, he's not out of shape, he's worked very hard this week and not recovered from the work he has done."
Giroud admitted to struggling to get to grips with the pace of the game, but feels he will be better prepared after another week of intensive training.
"It was really hard for me physically and I didn't feel really well in the game," he said.
"But it is OK as I have this week to work because we have to be ready for City.
"For pre-season preparation you have to work hard and there is less than one week to be ready."
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