Arteta confirmed Saka has had a hamstring operation after victory over Ipswich Town on Friday.
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He said, "He had a procedure.
"Everything went well, but unfortunately he will be out for many, many weeks.
"I said many weeks, so I think it will be more than two months. I don't know exactly how much longer.
"It will depend on how the scar tissue starts to heal, the first week or so, the mobility of that. Let's see, it's very difficult to say."
Meanwhile, Arteta has hopes of Raheem Sterling returning next week after suffering a knee strain.
"Yes, we have to see this week how he evolves," added Arteta. "We probably expected the knee injury to take longer than it has evolved in the last few days. Hopefully that's good news because we need him."