Three people were on board the boat near Russell Road, Shepperton, when it capsized at about 18:00 BST, a spokesman for Surrey Police said.
A man in his 40s and a teenage boy managed to get to safety and are believed to be safe and well.
A search for another man aged in his 40s has been called off for the night and will resume at 07:00 BST.
Firefighters and police had been searching the water and riverbanks for the man.
Two people have been rescued and one has been reported missing after a boat capsized on the River Thames in Surrey.