He started at Ohau Point, west of Wellington, about 8.30am and was about halfway across when he pulled the pin at about 4.40pm.
He had hoped to complete the 22km-26km swim to the South Island in about 8 hours.
The Tūhura Otago Museum board chairman and University of Otago physics professor was attempting the swim in a bid to raise money for a much-needed new fire sprinkler system at the Dunedin museum.
The swim aimed to highlight the critical importance of museums, history and protecting New Zealand's past and the financial pressure that many museums are under in the current economic climate.
He said Otago had an "exceptionally rich history", particularly during the gold-rush era, and it had allowed the museum to acquire a vast and internationally significant collection of more than 1.5 million items.
However, the museum was a charitable trust and only received modest support from ratepayers, and little to no direct central government funding, which left major gaps when it came to essential infrastructure, capital investment and collection care, he said.
One of the most urgent needs at present is the installation of further fire sprinklers to protect the museum's "irreplaceable collections".
Prof Hutchinson said the idea for the fundraising swim bubbled to the surface during one of his outings in Otago Harbour with the Sunday Swim Squad at Broad Bay.
"Swimming the Cook Strait felt like something I could do to highlight the circumstances in which the Museum Trust finds itself.
"Water is both the challenge and the solution."
• A Givealittle page to raise funds for the museum has been set up.
