Rudy Bruynius, who has been named online, was with wife Lisinda and their daughter McKayla when they were caught up by a large wave at Fistral Beach on the north-west coast of Cornwall on Saturday.
Mr Bruynius, who is originally from South Africa but was living in London, was taken to hospital where he was pronounced dead, while McKayla was reported to be in a critical condition.
Two other children in the family managed to scramble back on to the rocks, the RNLI said.
In an online post mum Lisinda said: "Please continue to pray for my miracle baby, for her to pull through."
A fundraising page, set up to support the family, has raised over £14,000.
Family friend Madelein Jansen Van Noordwyk posted a message from Lisinda which said: "Thank you all so much for your prayers!!!"
