Odum was placed on the Active/Non-Football Injury list (NFI) on Friday before the 49ers announced he was being released Saturday.
The 31-year-old signed with the 49ers in 2022 and played in 40 games (two starts) for the team. He finished his San Francisco career with a total of 50 tackles, 36 solo, five passes defensed and one interception.
In 2022, Odum earned Second-Team All-Pro honors for his work on special teams.
Odum went undrafted in 2018 before signing with the Indianapolis Colts, where he played the first four seasons of his career.
