L.A. sheriff's deputies said that the body was found in the concrete-lined channel near the 1700 block of Spring Street in the Lincoln Heights area just before 7:30 a.m.
The river level is currently shallow near the Spring Street Bridge between Chinatown and Lincoln Heights, and homeless people often camp in the riverbed.
The victim was identified as 21-year-old L.A. resident Pearson Kim Taing.
Anyone with information was urged to contact the L.A. County Sheriff's Department at (323) 890-5500. If you prefer to remain anonymous call Crime Stoppers at (800) 222-TIPS.
The Associated Press contributed to this report.