Coach Gary Kubiak says the 6-foot-5, 300-pound Harris was hurt during an individual period on Tuesday and will be placed on injured reserve.
Harris signed with Houston as an unrestricted free agent in January. He was originally a sixth-round draft pick by Pittsburgh in 2009. He was cut by the Steelers, claimed by Carolina and played in two games for the Panthers in 2009.
The Texans (No. 4 in the AP Pro32) play at New Orleans (No. 9) in the third preseason game on Saturday. Houston's defensive front has been dented by injuries -- nose tackle Shaun Cody is nursing a sore back and defensive end J.J. Watt dislocated his left elbow early in camp.