The former USC standout will be placed on injured reserve.
Cushing will have surgery to repair the damage in two to three weeks after the swelling subsides.
"Big blow to our team," Kubia told Houston reporters. "You feel bad for Brian because he works so hard and was playing so well."
Cushing was a second-team All-Pro selection last season.
He got hurt Monday night against the New York Jets when he was rolled over by offensive guard Matt Slauson during the second quarter.