Royal Caribbean International's Liberty of the Seas is sailing to Saint John, New Brunswick, and Carnival Cruise Line's Carnival Sunshine substituted an eastern Caribbean cruise with calls at San Juan, St. Thomas and Grand Turk.
Liberty of the Seas is based at Cape Liberty in Bayonne, New Jersey, and Carnival Sunshine at Port Canaveral.
Carnival said passengers will receive a 25% discount on their next next two- to eight-day cruise.
On Sunday Bermuda was experiencing tropical storm conditions and was under a hurricane warning. Joaquin's maximum sustained winds had decreased to near 100 mph (155 km/hr) with higher gusts.
Forecasters at the National Hurricane Center in Miami expect Joaquin to continue to steadily weaken in the next two days and become an extratropical cyclone as it moves over the cold waters of the far north Atlantic.