Coach Gary Kubiak announced the moves on Sunday, the day after the Texans' 23-7 preseason win over Dallas.
The 6-foot-1 Bennett was drafted by Houston in the fourth round in 2007. He played in 40 games and intercepted five passes in three seasons.
The Texans have drafted four cornerbacks in the past two drafts. This year's top pick, Kareem Jackson, is taking the starting role left when Dunta Robinson signed with Atlanta in the offseason. Kubiak said Sherrick McManis, Houston's fifth-round pick this year, has played well during training camp, so the team decided to cut Bennett.