Odom is the fourth Bengal to go on IR in the last two weeks, joining defensive tackle Tank Johnson, safety Chris Crocker and defensive lineman Frostee Rucker -- all of whom have knee injuries.
Odom was added to Cincinnati's active roster last week. The seventh-year pro had a one-week roster exemption after serving a four-game suspension for violating the NFL's ban on performance-enhancing drugs. He broke his wrist Oct. 10 -- his last game before the suspension.
Injuries have plagued Odom since joining the Bengals as a free agent from the Tennessee Titans in 2008 as a major acquisition to help the defense. A foot injury limited Odom to eight starts and three sacks in his first season with the Bengals.
Last season, Odom emerged as one of the NFL's best at getting to the passer with an NFL-record seven sacks in his first two games. He was tied for the league lead when he tore his right Achilles' tendon just six games into last season. He still led the Bengals in sacks with eight despite his injury. He missed time during training camp this year because of an illness and a sore knee.
Odom's roster spot was filled by defensive end Victor Adeyanju, who was released by the St. Louis Rams after this preseason. Adeyanju spent less than one week with the Bengals last month before being cut.
Sunday's game against the New Orleans Saints will be blacked out on local television after failing to sell out by the NFL deadline.