The company does not know yet how extensive the damage to the ship's engine is, or how it could affect future voyages.
"We know this has been an extremely trying situation for our guests, and we sincerely thank them for their patience," said Gerry Cahill, president and chief executive officer of Carnival Cruise Lines. "Conditions onboard the ship are very challenging, and we sincerely apologize for the discomfort and inconvenience our guests are currently enduring."
Carnival said it would provide passengers a full refund for the current trip and would offer a complimentary future cruise "equal to the amount paid for this voyage."
The ship was on the first leg of a seven-day cruise on the Mexican Riviera. It departed from Long Beach, Calif., Sunday. It was scheduled to stop in Puerta Vallarta, Mazatlan and Cabo San Lucas, then return to Long Beach.
Carnival is the world's biggest cruise ship operator with lines including Holland America, Princess and Cunard.
Another Carnival ship was stranded with more than 2,000 passengers this summer due to a "technical malfunction." The problem was fixed within hours, however, and the ship was able to complete it's trip about three hours behind schedule, according to a report by USA Today.
In 2006, a fire on the Star Princess cruise ship, which is run by Princess Cruises, killed one person and injured 11 others. At least 100 rooms were scorched, but the nearly 3,000 passengers did not have to abandon ship.
In 2003, eight crew members aboard Norwegian Cruise Lines' Norway died in an engine-room explosion.
Carolyn Brown, editor-in-chief for CruiseCritic.com, said that the passengers of the Splendor were actually lucky the engines stopped functioning so close to the coast, rather than further out in open ocean and that the situation looks to be under control.
"Let's put it this way, nobody was injured. They're handling it," Brown told ABC News. "It's not ideal, and certainly it's not what you want to do on your vacation, but frankly, these people are going to have some stories to tell and I think they'll be good dinner party guests for decades to come."