Tight end Julius Thomas, who leads the NFL with 12 touchdown catches, hurt his ankle in the first quarter. Wide receiver Emmanuel Sanders, who caught a 42-yard touchdown pass Sunday, later suffered a concussion on a hard hit from Rams safety Rodney McLeod on the opening drive of the second half.
McLeod was flagged for unnecessary roughness on the play. Sanders is the Broncos' second-leading receiver, entering the game with 62 catches.
Denver backup running back Montee Ball also aggravated a groin injury that sidelined him for five games.
Dansby, who entered the game leading Cleveland in tackles, pounded the ground in frustration after going down. He is scheduled to undergo an MRI on Monday.
Browns coach Mike Pettine indicated Dansby's injury layoff could be long term.
Without Dansby, the Browns struggled to stop the run in the second half and the Texans rolled up 211 yards rushing.
Dansby has had a major impact in his first season with the Browns, who signed the 11-year veteran as a free agent in the offseason. Cleveland is already without massive end Phil Taylor, putting further stress on Cleveland's front seven.
He will have an MRI on Monday.
The two-time Pro Bowl selection was blocking on a third-down play when Bucs defensive lineman Gerald McCoy accidentally hit the back of his leg.
Williams and McCoy were good friends and college teammates at Oklahoma and were drafted consecutively in the first round in 2010.
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