The ship left Charleston on Feb. 15, the first departure in a newly-expanded year-round schedule of cruises from South Carolina as the industry expands in the state.
Martinez says the crew is conducting "enhanced cleaning" of the ship to prevent the spread of the illness.
An extra doctor and two nurses came aboard in St. Kitts, in the Leeward Islands, and will sail to Charleston, arriving early Friday.
It's not clear what caused the outbreak. Norovirus is often to blame for similar symptoms sweeping closed quarters like those on cruise ships, but a determination will have to until samples, which were being dropped off in Puerto Rico, are tested.
According to the Centers for Disease Control Web site, there were two outbreaks of norovirus, which causes stomach flu, last winter on the Celebrity Mercury. In all, the agency investigated 15 outbreaks of gastrointestinal illnesses on cruise ships calling at American ports.
A CDC spokesman did not immediately return a phone call from The Associated Press.
This year an estimated 14.3 million passengers are expected to take cruises, according to the Cruise Lines International Association, an industry trade group.
The South Carolina cruise industry is growing and the Mercury sailing earlier this month began Charleston's first year-round cruising season. There will be 67 cruise calls in the city this year.
The Celebrity Mercury has six more departures set from Charleston during the coming months, including a 16-night trip through the Panama Canal ending in Los Angeles.
Later this spring, Carnival Cruise Lines will permanently base its 2,056-passenger Carnival Fantasy in Charleston.
As the industry grows, the South Carolina State Ports Authority is pursuing plans to open a new cruise terminal and open another half-mile of Charleston's historic waterfront to the public.
A recent study commissioned by the authority shows cruises will mean $37 million to the South Carolina economy this year.