CBS News Correspondent Byron Pitts reports the disclosure was made in a case involving a former employee who claims she was viciously attacked and that Carnival tried to cover it up.
In the case, Carnival was forced to admit for the first time publicly that it had investigated 62 alleged sexual assaults in the last five years. The lawyer for the woman who filed the civil suit called the case the tip of the iceberg.
"Sixty-two is an extraordinary number of alleged sexual assaults to have happened in a five-year period," Gary Fox told CBS News. "And this is just by crew members. Keep in mind that these statistics don't include rapes to passengers by other passengers."
Still, Carnival Cruise Lines maintains its ships are safe, pointing out cruise ships are not required to report crimes to U.S. authorities when they occur in international waters.
"You have to look at things in context," insisted Carnival attorney Curtis Mase. "Carnival carried over 6.5 million passengers during the five years we're talking about.
"The number of alleged incidents - and bear in mind that it is a list of allegations, not necessarily substantiated incidents - includes everything from sexual harassment complaints by crew to an unwanted kiss to matters of a more serious sexual nature," Mase said. "Many of the incidents do not involve alleged rape."
Pitts reports this lawsuit also raises questions about old allegations that Carnival and other cruise lines aren't helpful investigating reports of assaults or other incidents aboard ship.
"I have investigated sexual assaults, rape, child molestation on the ships," former Carnival security chief Charles Harris told CBS News. "In the cruise lines industry in general, the idea is to protect the company first and worry about the victim later."
Fox, the attorney for the woman, charged "Carnival tried to cover it up and assisted the perpetrator in fleeing the country back to Italy before the FBI could question and detain him."
But Mase said the assailant in her case, Italian engineer Yurij Senes, was fired for drinking within six hours of going on duty and for being tardy. He said that Senes was sent to Italy "in accordance with federal repatriation laws" for fired workers.
Senes was charged in September with one federal count of rape on the high seas, a crime punishable by up to 20 years in prison, said U.S. Attorney Jennifer Prior in Miami. Trial is set for November.
The woman is seeking unspecified damages and wants Carnival to supply ships with special kits for rape victims and to assist prosecutors' efforts to win Senes' extradition.
Elizabeth Cummings' 19-year-old daughter died while swimming on a Carnival cruise ship nearly two years ago. The company, the mother says, ws more concerned about its reputation than her daughter's safety.
"We always had thought of a cruise ship as the ideal vacation," Elizabeth Cummings told CBS News. "I would never set foot on a cruise ship again."
As for this latest allegation of sexual assault, the case could go to trial in November.
When accused last fall of covering up assault claims, Carnival responded by saying it is "at least 10 times more likely for a sexual assault to occur in a small town in America than on a cruise ship."