Simon got hurt against the Oakland Raiders on Monday night in Mexico City, leaving the game and not returning.
Simon ranks second on the Texans' defense with 50 tackles and 3.5 sacks.
"Our team has really taken the mantra of 'next man up,' and that's what it's going to have to be with John because he'll be out for a bit," Texans head coach Bill O'Brien said. "He's a very tough individual. Somebody is going to have to step up. Different people are going to have step up in his role and play well for us."
Simon was replaced at outside linebacker by backup inside linebacker Akeem Dent. Primarily a special-teams contributor, Dent is a former defensive starter who has two tackles this season on defense.
The Texans also shifted starting defensive end Jadeveon Clowney over to his natural outside linebacker spot at times late in the game.
"Akeem got in and played a little bit later in the game," Texans defensive coordinator Romeo Crennel said. "Clowney was outside a couple of times as well. So, we try to mix things up a little bit depending on what they're doing and what we have to face."