Brown will be allowed to participate in training camp and preseason games, but will not be on the active roster for the season opener against the Oakland Raiders or for the Rams' Week 2 matchup against NFC West rival Arizona.
Brown, a fourth-year pro, can return to the active roster on Sept. 17 in preparation for the Rams' Week 3 game against the Los Angeles Chargers.
In a statement released on Twitter, Brown apologized and explained that an "isolated mistake" 18 months ago led to his suspension.
His suspension is a considerable loss for a team that is looking to win a second consecutive division title and is considered a Super Bowl contender.
Last season, Brown started 16 games as the Rams became the only team in the NFL to start the same five linemen for 15 consecutive weeks. The group allowed 28 sacks and helped spring running back Todd Gurley for 1,305 yards rushing and 13 touchdowns.
Third-year pro Austin Blythe is among the candidates to start in place of Brown. Last season Blythe saw time at center and guard.
The Rams open training camp July 26.