Coach Jeff Fisher confirmed the extent of the injury Sunday night, news first reported by ESPN and the St. Louis Post-Dispatch.
"We lost our quarterback," Fisher said. "For Sam, it was devastating."
In all, five starters were hurt against the Browns.
Cornerback Trumaine Johnson was carted off with a knee injury and three others — guard Rodger Saffold and defensive tackles Kendall Langford and Michael Brockers — left with ankle injuries.
Johnson will be out 4-6 weeks with an MCL tear, but Fisher said Saffold, Langford and Brockers could play if needed in the preseason finale Thursday at Miami.
Bradford was injured in the first quarter of Saturday night's 33-14 preseason victory at Cleveland. He was hit on his left side by Browns defensive end Armonty Bryant as he threw a pass.
Bradford hopped briefly on his right leg before dropping to the ground.
Bradford, the first overall pick of the 2010 draft, missed the last nine games last season after getting injured at Carolina. Veteran Shaun Hill is the backup and the Rams also have rookie Garrett Gilbert and Austin Davis on the roster.
"Shaun's our guy," Fisher said. "I brought him here."
After the game, Fisher thought Bradford might have hyperextended the knee and was "very optimistic." Bradford walked off the field, and then walked to the locker room after the injury.
Wide receiver Brian Quick said he was assured by the quarterback that he was "OK."
"It is a tremendous loss for them," Browns coach Mike Pettine said. "We knew that it didn't look like much when it happened, but I just think it was a good amount of weight that got put on it. It's such an unfortunate thing."
Pettine said there "certainly wasn't any intent" by Bryant to hurt Bradford.
Bradford had 14 touchdown passes and four interceptions last season. The Rams then upgraded their offensive line by drafting guard-tackle Greg Robinson No. 2 overall.
Bradford played in two preseason games and was 4 for 9 for 77 yards against the Browns.
The 34-year-old Hill has thrown only 16 passes the past three seasons as the backup in Detroit. He made 10 starts in 2010 for the Lions in place of injured Matthew Stafford and beat the Rams for Detroit's first win after a 0-4 start.
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