The Texans fear the injury is a torn ACL, but they will not know for sure until his MRI Tuesday, said a source familiar with the situation.
Cushing left in the second quarter and did not return. Cushing led the Texans with 38 sacks entering the game. He was the 2009 Defensive Rookie of the Year.
"I don't want to jump the gun," Kubiak said. "He'll get it looked at when we get home and we'll hope for the best.
"I don't know what happened. They tell me he cut on the play and his foot might have got stuck in the turf."
Cushing will undergo the MRI in Houston, according to the Houston Chronicle.
Several Texans worried that Cushing's injury could be long-term.
"This is a physical game that we play," safety Danieal Manning said. "We're a physical team and you tend to have those kind of injuries. They kind of go with the territory."
New York lost starting center Nick Mangold in the third quarter to a right ankle injury. He was carted to the locker room but returned for the final play of the period.
Gates said his shoulder was popped back into place and he expected to be fine.
Jets defensive tackle Kenrick Ellis injured a knee in the fourth quarter.
Information from The Associated Press was used in this report.