The 25-year-old Ghanaian was injured during the Serie A champions' 2-0 win at Empoli on Saturday.
Asamoah featured in Tuesday's 3-2 UEFA Champions League victory against Olympiacos, but will play no part against Parma on Sunday.
A statement on the club's official website said: "Kwadwo Asamoah will be out for a precautionary period of 15 days in order to fully recover from the injury he sustained during last Saturday's Serie A meeting with Empoli.
"The Ghanaian featured in last night’s game against Olympiacos but continued inflammation in his knee means he will be rested over the next couple of weeks."
The Turin giants will be hoping Asamoah is able to return for the clash against Lazio on November 22.
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