Police said a boy on the bank saw his father's boat capsize on the River Wey in Guildford at about 13:10 BST on Monday.
Insp Claire Sutherland said the boy jumped into the fast-flowing river to try to save him but members of the public shouted to come back.
Divers are trawling the river in Millmead.
Members of the public have been urged not to go into the water if they spot the missing kayaker, but to call 999 immediately.
A flood warning is in place for parts of the River Wey, following heavy rain and storms over the weekend.
A police helicopter, firefighters and ambulance crews were all at the scene on Monday.
The river from Millmead to Stoke Lock is a popular with kayakers.
Wey Valley Kayak Club, which has about 400 members, is situated about about one mile down river from where the man capsized.
It tweeted on Monday morning the Wey from Godalming Wharf to Thames Lock was not safe.
A search has resumed for a man missing after his kayak overturned on a river in Surrey.