The police patrol boat departed Rarotonga for the north late on Saturday morning upon being secured by the Ministry of Health under a special charter.
A doctor and a nurse are also aboard Te Kukupa to attend to the patient when it reaches the island.
The boat is reportedly in calm waters and was due to arrive at Nassau yesterday evening.
Te Kukupa is expected back at Avatiu wharf by late tomorrow.
In February the patrol boat was called out on an emergency rescue when the yacht Zangona reported hitting a submerged object and began taking water. It was later found the vessel had been deliberately sabotaged.
And in September Te Kukupa was sent on a night mission to rescue seven fishermen who went missing in rough seas near Manuae.
Manuae is an uninhabited island near Aititaki.
The fishermen were found – tired, but safe – and two of their fishing boats were brought on board the patrol boat. A third vessel had sunk.