Martin Odegaard and Bukayo Saka both pulled up short during the 5-0 win on Saturday.
Afterwards, Arteta said: "Martin felt something in his shoulder when he landed, we don't know but we have to scan it tomorrow so we can understand it a bit better.
"With Bukayo, while he was running with the ball, carrying the ball and wrestling with the defender, he felt something in his hamstring. Let's see, it's not the same one as the previous injury but we're two weeks in and we've already lost Kai (Havertz), Martin and Bukayo so it tells you how well equipped you have to be in this league to maintain the level you want.
"Bukayo felt something while he was sprinting which is never a good sign but we have to wait until tomorrow He's had his injuries before so he knows the feeling of that, so let's wait."
Arteta also added in a separate TV interview: "For Bukayo to come off, for sure it looks like something that is significant."