Tomiyasu got a scare last week when he limped off against FC Zurich in the Europa League with a muscle problem.
And he is not expected to feature against Brighton in the Carabao Cup on Wednesday.
Arsenal continue to assess the right-back but the initial diagnosis is promising and there are hopes he can play for Japan at the World Cup.
The Japanese FA have been in contact with Arsenal since Tomiyasu’s injury and continue to be.
“It’s a small injury for Tomi, he did well to stop during the game, so it won’t be a big problem,” Arteta said.
“I think he’ll be back in about a week, so hopefully he’ll be fine to start the World Cup.”