"The passenger was identified as a close contact of a confirmed case on land, and was immediately isolated as part of onboard health protocols," the tourism board said in a statement.
It said the 40-year-old passenger tested positive to a Polymerase Chain Reaction (PCR) test onboard and had been conveyed to hospital for further confirmatory testing.
The guest had tested negative during the mandatory pre-departure antigen rapid test on July 11.
The passenger's three travelling companions were identified and isolated, the tourism board said. They have tested negative for COVID-19 and further contact tracing was being done.
All on-board leisure activities on Dream Cruises' World Dream ship had ceased and passengers had been asked to stay in their cabins until test results are out and contact tracing was complete, the tourism board said.
Contactless meals were being sent directly to their cabins.
Several guests aboard the docked ship were chatting with one another across their private balconies.
Genting did not have an immediate comment.
The ship left Singapore on Sunday for a four-day cruise, according to a media report.
The global cruise industry has taken a major hit from the coronavirus pandemic, with some of the earliest big outbreaks found on cruise ships.
Singapore, which has seen relatively few domestic COVID-19 cases, launched "round trips" on luxury liners in November, which have no port of call and last only a few days.
Such cruises have become popular during the pandemic and are restricted to Singapore residents.
Last December, passengers on Royal Caribbean's (RCL.N) Quantum of the Seas vessel were held in their cabins for more than 16 hours after a suspected COVID-19 case on board which turned out to be a false alarm. Reporting by Chen Lin and Aradhana Aravindan in Singapore; Writing by Ed Davies; Editing by Christopher Cushing, Robert Birsel, Richard Pullin