They were planning to tow the ship to Ensenada, officials said.
Nearly 3,300 passengers are onboard the vessel. They were forced to move to the upper deck of the cruise ship to open air after the fire broke out about 6 a.m. Monday, officials said.
"Conditions on board the ship are very challenging and we sincerely apologize for the discomfort and inconvenience our guests are currently enduring," said Gerry Cahill, president and chief executive officer of Carnival Cruise Lines.
The ship sits in open water about 55 miles west of Punta San Jacinto, Mexico. Sea conditions are calm.
Passengers boarded the /*Carnival Splendor*/, along with nearly 1,200 hundred crew members, and left from Long Beach on Sunday on the first leg of a seven-day Mexican Riviera cruise.
"The fire has been extinguished," Carnival said in a statement earlier Monday. "No injuries to guests or crew have been reported. Currently, the ship is operating on emergency generators and the ship's crew is working to restore power to the vessel. The decision has been made to terminate the voyage."
People preparing to leave on a different Carnival cruise ship Monday afternoon were surprised to hear about the fire, but felt safe boarding.
"I think if it's going happen, it's going to happen," said Lori Brefeld of Paso Robles. "We got here safely by the grace of God in a car."
"We'll get on the cruise ship and they'll go over all the safety and what will happen if something happens, so I have no worries getting on the cruise ship now," said Tianna Speth of Paso Robles.
The ship was to return to the port of Long Beach.