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Wilshere was bodychecked by Alfred N'Diaye midway through the second half of the game at the Stadium of Light, before being helped from the pitch.
Meanwhile, the centre-back was a late withdrawal from the matchday squad after aggravating his calf in the warm up.
But Wenger has tempered fears of an extended period on the sidelines for the pair.
"[Koscielny has a] calf problem. We think it's a question of days because he had a positive scan.
"He limped out with the French national team and we decided to give him a try in the warm up but it was not good enough but I don't think it's long term.
"Jack is a big kick on the thigh, he could not walk. Again it's just a question of four or five days."