Eyewitnesses described seeing police, paramedics, and the fire brigade at the scene on the bridge shortly after midday.
It was later confirmed that one of the two men involved in the incident was pronounced dead at the scene, while the other man has been taken to hospital.
An update on his condition is yet to be provided.
A Met Police spokesman said: “Officers were called at 12.35pm on Monday, September 9, to Kew Bridge Road to concerns for safety.
“Officers, LAS and the RNLI attended the scene where two males were found in the water.
“Both males were pulled from the river.
“One male was pronounced deceased at the scene.
“The other was taken to a west London hospital. We await for an update on his condition.”