"Three crewmembers and two contractors who were working onboard were transferred to a local medical facility. We are deeply saddened to learn that two contractors and one crewmember did not survive. We extend our deepest condolences to their families during this very difficult time.
Arrangements are being made for guests and crew to be accommodated at local hotels until transportation to Miami is arranged."
The fire is believed to have started shortly before 9:30am local time, after the ship lost power and the local fire service was contacted.
Insignia was on a 10-night voyage from San Juan to Miami and was scheduled to arrive in Florida on December 17.
The ship will remain in St Lucia, until local authorities have assessed the incident. Guests are remaining in hotels, until they can be flown to Miami.