Tali Lennox was rescued from the Hudson River but Ian Jones, a photographer, went missing after the vessel flipped near Mills Mansion, a historic home in the hamlet of Staatsburg.
Lennox, 22, a model and artist, was saved by a passing vessel, but despite a 12-hour search Mr Jones, 32, was not found.
The Poughkeepsie Journal said Lennox, also known as Tali Fruchtmann, was not injured and did not require hospital treatment.
Rescuers do not suspect foul play. Police say alcohol may have contributed to the accident.
A spokesman for the Aberdeen-born singer, 60, yesterday said he just heard about the accident and was trying to get more information.
Police said Tali Lennox had been picked up by passers-by on a boat after being separated from Jones in the water.
The two were reported to be not wearing lifejackets when the kayak flipped.
The accident happened not far from where another kayaking problem evolved into a murder charge earlier this year, authorities said.
Staatsburg is about 60 miles north of the area where kayaker, Vincent Viafore disappeared during a kayaking trip with fiancée Angelika Graswald on 19 April.
She told authorities his kayak capsized accidentally and she could not save him. But prosecutors say she admitted tampering with his kayak to cause his death.
Graswald has pleaded not guilty to a murder charge.
Earlier this year Lennox, who has modelled for the likes of Topshop and Burberry in the past, spoke of how her career is now more focused on her art.
“I’ve not given up modelling. It’s just that I’ve gone down different paths at the same time so I’m much more focused on my painting,” she told Hello! Fashion magazine.
“Modelling’s great. Now I’m at a place where I can be more selective.”
She added that she would hate to be viewed as a stereotypical child of a star.
“I’m very proud of my mum but it propels me to want to show people who I am,” she said.
“And it definitely accelerates my need to not want to be a cliché.
“[By that I mean] being spoilt and talentless. Just hanging out and not doing anything. That’s not me at all.”
She said she did not accept help from her mother when she started out in modelling.
She said: “[I wanted to] start work from scratch. I want to work hard for what I have because, also, I think where’s the satisfaction in not feeling like you have to strive for something?
“It’s in my blood. We were brought up unconventionally in some ways - being surrounded by creative people - but in other ways it was very normal.”