Martinelli was forced off in the first-half of Sunday's win at Everton.
Arteta said: “He felt something in his hamstring and we need to do some further tests to assess if there is any big damage or not, but he will be out for tomorrow's game (against PSV), that's for sure."
The manager also delivered an update on Mohamed Elneny's recovery from a back strain.
“He's in a good place, obviously it's been a while and it's been a very significant injury, but I think he's in the latter stages of that rehab process.
“He's been training for almost two weeks with the team and he is in a good place. It's always great to have him around."