He will not require surgery.
Bulger was hurt when he was sacked by Antonio Cochran and John Hilliard three minutes into Sunday's 30-10 loss at Seattle. A CT scan revealed no broken bones and Bulger will not require surgery, but will need to rest for 6-8 weeks.
"It's painful for him, but it's not going to hinder his career or affect him in any way," said Rams Coach Mike Martz of Bulger's injury.
On Sunday, Bulger was trying to become the first quarterback to win his first seven NFL starts since Minnesota's Daunte Culpepper in 2000, but attempted just one pass before the injury. Jamie Martin replaced Bulger and threw for 259 yards and a touchdown, but was intercepted three times.
Scott Covington is the only other quarterback on the Rams roster. St. Louis lost starter Kurt Warner to a broken hand in a Dec. 1 loss at Philadelphia.
Bulger was 6-0 as a starter filling in for Warner this season, but also was sidelined for a few games with a sprained finger ligament. He has completed 64 percent of his passes for 1,826 yards and 14 touchdowns with six interceptions.
The Rams (6-9), who missed the playoffs for the first time in four years, will also be without starting linebacker Tommy Polley and defensive end Grant Wistrom for the season finale against San Francisco. Polley has a high ankle sprain and Wistrom a hairline fracture in his right leg.
Celebrity Breakups and divorces of 2014 [PHOTOS]