Origi, who plays for Moss FK of Norway, sustained the injury during the Harambee Stars' 2-0 win over the Warriors last Saturday.
The result took Kenya to the top of Group Two of the joint 2010 World Cup and Africa Cup of Nations qualifiers.
Origi underwent a successful operation on Sunday and will be out of action for six to eight weeks, doctors said.
He will still travel with the team to Harare for the match.
Either Joseph Ruto of Tusker or Gor Mahia's Jackton Odhiambo will take over between the posts.
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