The force is currently at the scene along with South East Coast Ambulance Service (SECAMB) and Surrey Fire and Rescue.
A SECAMB spokesperson said earlier that three of the five rescued from the river were taken to hospital for further checks.
Surrey Police statement latest.
We, along with other emergency services, were called to Sunbury Lock near Wheatleys Eyot at around 8.50am this morning (11 October) after a rowing boat capsized.
It was reported that six adults entered the water.
Five of those people have since been safely located and accounted for.
Sadly, we believe a man in his 60s may still be in the river.
His relatives have been informed and are being kept updated.
At this time, enquiries to establish the full circumstances of what occurred remain ongoing.
Chief Inspector for North Surrey, Andy Jenkins said; “This is a very distressing time for all involved and we continue to support our partners in the search for the missing man.
“Our enquires to establish the exact circumstances of how the boat capsized remain underway but at this time we do not believe there to be any suspicious circumstances or third-party involvement.
“We will look to share any further updates with you as and when we have them.”
The lock and this part of the river are busy and popular with water sports activities but access is inaccessible from the road and can be reached along the towpath from The Weir Hotel or Elmbridge Leisure Centre on the Walton side.