Houston, who won't need surgery to repair the injury, was injured in the first half of the team's 41-38 loss to the San Diego Chargers. Houston was seen in the Chiefs locker room earlier this week with his arm in a sling. According to the report, an MRI revealed sprained ligaments and torn muscles in the elbow.
He was unlikely to play in this week's pivotal AFC West matchup against the Denver Broncos.
The Chiefs are second in the division and have lost two straight games after winning their first nine. The Chiefs other injured linebacker Tamba Hali said Wednesday he should be good to go to play on Sunday.
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A three-week absence for Houston would leave Kansas City vulnerable this Sunday against the Denver Broncos, but the following two weeks bring the beatable Washington Redskins and Oakland Raiders. The Chiefs -- even with Houston and Hali in the fold -- haven't rushed the passer as effectively over the past month, but this remains the AFC's most dangerous duo of outside linebackers.