The Ghana midfielder hobbled off during Sunday's 2-0 loss to Tottenham.
But Partey did not re-injure the same thigh which kept him out for a month prior to the Spurs game.
"He got injured in the same area, but not in exactly the same spot as before," Arteta said ahead of Thursday's Europa League group game against Dundalk.
"He had an MRI yesterday, there is an injury there, he will miss the next few matches.
When asked if it was an unnecessary risk to rush him back from injury, Arteta said: "No, he did incredibly well, he was confident. We tested him three times and he had no symptoms.
"But in football you have a lot of unpredictable actions. He went into the floor, his knee got stuck, after he needs to stretch and get up up. Immediately he put a lot of stress in a similar area and he felt it again."