Johnson suffered a broken foot in Houston's overtime win over the Indianapolis Colts last weekend.
A former first-round draft pick out of Wake Forest in 2015, Johnson started and played well against the Colts. The Texans have been ravaged in the defensive backfield, but are hopeful that corner Johnathan Joseph (forearm) will return to the lineup for Monday's game versus Denver.
To fill Johnson's place on the roster, Houston activated safely Lonnie Ballentine from the physically unable to perform list. Ballentine has been sidelined since suffering a knee injury last season.
Johnson is among four players ruled out for the Texans on Monday, joining safety Quintin Demps (calf), linebacker Brian Peters (quadriceps) and running back Jonathan Grimes (ankle).
For the Broncos, outside linebacker DeMarcus Ware will miss his fifth consecutive game due to a fractured forearm.
Ware was injured in a Week 2 victory over Indianapolis and has not practiced since.
Denver is still waiting to see on the availability of left tackle Russell Okung and wide receiver Cody Latimer, who are in the league's concussion protocol.
Both players are scheduled for a final league-mandated examination in order to be cleared to play.