Narok county police commander John Kizito said members of the public had spotted the body near Narok town.
The commander said the body had no visible injuries and suggested the man had drowned in the upper part of the river and his body was swept downstream.
The man has not been identified. Police called on members of the public with missing relatives to report to the police so the victim can be identified and given a decent burial.
The body is at the Narok County Referral Hospital mortuary, awaiting postmortem and identification.
Cases of drowning have been rampant in the area as many rivers are swollen following the downpour throughout the entire county.
Last week, a lorry transporting fuel to a Maasai Mara National Reserve petrol station plunged into River Mara when the driver was trying to cross the swollen river.
One occupant escaped unhurt, one person died and the body was recovered. The driver was swept away by the raging water and his body is yet to be recovered.
The county security team has warned motorists and pedestrians not to attempt to cross a swollen river no matter how small it may appear.
Kizito said most points that look shallow and calm are the most dangerous points as they could be deep.
He warned parents against sending their children to graze livestock in areas far from their homes. He said sometimes it rains heavily in the afternoon causing seasonal rivers to rise. They are dangerous to cross.
(Edited by V. Graham)