He will undergo an MRI to confirm the tear.
Miller was taken off the field on a cart during the first quarter in Arlington, Texas.
On first down, Miller was tackled by Cowboys tackle Maliek Collins, who hit him just above the left knee. Miller, 28, grabbed his left leg and was checked out by the medical staff. He was eventually carted off the field.
"It was a tough thing to see," Texans coach Bill O'Brien said of Miller's injury. "It's very difficult to lose a guy like Lamar, for a lot of reasons. He's a great pro. He's just an awesome guy in the locker room."
Quarterback Deshaun Watson echoed his coach.
"It's very tough. You have a guy that is so special to our team," Watson said. "[When] anybody gets hurt, it's tough. But he's one of the guys that has a lot of energy and a lot of power for this team. And, I mean, it was tough to see him go off on the cart."
Miller has been the Texans' lead back since 2016. In 14 games last season, he ran for 973 yards on 210 carries and scored five touchdowns. Miller is entering the final season of a four-year contract.
O'Brien said he isn't sure yet how losing Miller will affect playing time for Johnson but said, "I think our backfield situation with depth is actually decent."