The injury occurred in the fourth quarter of his side's defeat to the New England Patriots, when he celebrated notching a sack of backup quarterback Jimmy Garoppolo with the score at 48-23.
The Bears also lost offensive lineman Matt Slauson for the season with a torn pectoral muscle he suffered in the same match.
"He let out all of his frustrations and ultimately paid a price for it," general manager Phil Emery told reporters of Houston. "We're disappointed for him and in him."
Houston had recorded 11 tackles and one sack for the Bears since his off-season move from the Oakland Raiders.