The woman, who is in her late 60s, had a medical event on Emerald Princess around 10:00 a.m. on Sunday.
She has been transported ashore to Port Chalmers on one of the ship's tender vessels to receive medical attention, St John's Ambulance advised.
The ship's arrival into Dunedin on Sunday was delayed by two hours due to heavy fog.
The Emerald Princess is currently the subject of two investigations after a gas cylinder explosion on board the vessel killed one of its crew earlier this month.
Technical work on the hydraulic launching system of a tender vessel has been suggested as a cause of the explosion.
Two Transport Accident Investigation Commission (TAIC) investigators completed work on board the ship before it departed Port Chalmers for Sydney in early February.
That investigation was ongoing. The second investigation concerns the ship striking a rock in Milford Sound the same day as the fatal explosion.