The company said it was treating the illness as a Norwalk-like virus, the same type of illness that has sickened hundreds of passengers on other cruise ships in recent months.
The Conquest had left New Orleans on Dec. 8 with 3,160 passengers.
Carnival said it was working with the federal Centers for Disease Control and Prevention to determine the source, but company officials said they believe the virus was carried onto the ship by a passenger who reported feeling sick two days before the ship left port.
"All it takes is one guest to get on and pass it onto other guests," said Steve Williams, director of Carnival's medical operations.
Sick passengers stayed in their cabins to contain the virus and the buffet area was closed during the voyage, Williams said.
On Sunday, cleaning contractors and crew members disinfected the 110,000-ton passenger ship, the newest in Miami-based Carnival's fleet, he said.
The ship then departed that evening on its next seven-day cruise, to the western Caribbean. Four people canceled their Sunday voyage and 38 people didn't show up for departure. Carnival said it informed passengers of the outbreak and offered refunds to any who did not want to sail.
This year has seen a rash of viral outbreaks on cruise ships.
"This is not a new super bug that has suddenly come on," said Williams.
Williams said the Conquest's stomach ailments were probably caused by a Norwalk-like virus, also called NLV. He said the virus is showing up more frequently throughout the United States and Canada.
The Norwalk and Norwalk-like viruses — which cause diarrhea, stomach pain and vomiting for up to 48 hours — are spread by close contact with infected people or the things they have touched.
"You can't put it in perspective until you understand how common it is in the general population," said Tim Gallagher, a Carnival spokesman. "When you see a spike in the NLV on cruise ships, that means there's a spike in the general population."
Williams said cruise lines, unlike schools or hospitals, are required to report outbreaks of the viruses to the Centers for Disease Control and Prevention, which makes it seem like the viruses flourish on cruise lines.
"When you talk to the CDC this is not something confined to cruise ships," Gallagher said.
The CDC reports that the viruses make 23 million people sick in the United States each year.
The CDC is looking into over 20 outbreaks on cruise lines, more than it has seen in the four previous years combined. The agency considers an outbreak to be 3 percent or more of a cruise ship's passengers or crew members getting an illness.
Federal health officials are telling cruise lines to carefully clean their ships and to remind crew members and passengers of the importance of frequent hand-washing to avoid the viruses.