A sixth-round draft pick from Ohio State, Fuller started the first three games of the season but suffered a shoulder injury in a Week 3 loss to the Buffalo Bills and was inactive the Rams' victory in Week 4 against the New York Giants.
Fuller returned to the starting lineup in a 30-10 win over the Washington Football Team in Week 5, but injured the same shoulder when he tackled running back J.D. McKissic during the final defensive series.
"It's his right side," Rams coach Sean McVay said. "He had a little stinger. It's more of his neck, kind of, just having a stinger, but it is on the right side."
Second-year pro Taylor Rapp, who started 10 games last season and started in Fuller's absence in Week 4, is expected to start when the Rams (4-1) play the San Francisco 49ers (2-3) at Levi's Stadium on Sunday Night Football.
In a pair of corresponding roster moves, the Rams promoted defensive back Juju Hughes from the practice squad to the active roster and signed defensive lineman Eric Banks, who was waived last Saturday, to the practice squad.
In five games, Rapp has 24 tackles and a pass deflection. Fuller, who has has two pass deflections and 21 tackles in his four starts this season, is eligible to return from injured reserve after three weeks.