The Frenchman headed in Les Bleus' equaliser against Spain to earn a 1-1 draw and end La Roja's run of 24 consecutive wins in World Cup or European Championship qualifying.
Arteta now hopes that his teammate can take that belief into the Gunners' game with Norwich City at the weekend.
"I'm happy for him because he has a lot of pressure here, that comes from replacing [Robin] van Persie", Arteta told French radio station RMC.
"But he works very hard and I'm happy for him.
"Confidence will come [for him] and it will be good for [Arsenal] too."
Giroud scored his first Premier League goal for the club in their last outing against West Ham United.