Jackson signed the 34-year-old Odom near the end of last season in a reunion from their days together with the Los Angeles Lakers.
"Unfortunately, Lamar was unable to uphold the standards to return as an NBA player," Jackson said in a statement. "We found it necessary to free up the roster spot."
Odom has struggled with personal issues in recent years, but the Knicks did not indicate whether the split was due to on-court or off-the-court performance.
Aldrich played in 46 games for the Knicks last season and averaged 2.0 points and 2.8 rebounds.