The ship would be "comprehensively sanitised and cleansed" once it arrived at its next port of Sydney and before new passengers board.
Tasmania Director of Public Health Mark Veitch said five people from the ship were taken to hospital for check-ups.
"Outbreaks of highly infectious conditions such as gastro and respiratory illness can occur in cruise ships, where a population the size of a medium-sized town mixes closely together," he said.
Ovation of the Seas is expected to leave Sydney tomorrow on its next cruise before stopping in at Fiordland on Sunday, Dunedin on Monday, then Wellington, Napier and Picton before returning to Sydney next Thursday.