Netherlands international Van Persie has already spent time on the sidelines this season because of a groin strain, but made his first appearance since November 10 in the 1-0 defeat to Newcastle United last Saturday.
The former Arsenal striker also featured in the UEFA Champions League win over Shakhtar Donetsk on Tuesday, but will now be unavailable until January after sustaining the injury in that game.
"Robin Van Persie is out as well for a month," Moyes said.
"He picked up a thigh strain in taking a corner kick which led to the goal."
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