Port Health Authorities said the Belfast-bound Stena Line ferry could not leave Birkenhead after six members of staff were found to have coronavirus.
The 322 passengers and 53 crew have been told by public health authorities to disembark in Birkenhead.
Stena Line said it was helping passengers find alternative travel.
Passenger Alan Cogan said he was waiting for a replacement ferry to take him home to Northern Ireland, but said the delay meant he had to cancel a work video conference meeting.
The 47-year-old, who is an area manager for a heating company, said passengers “had resigned themselves” to being stuck and “were waiting to see what happens”.
He said tensions were initially high when a public announcement was first made at about 3:30 GMT, more than five hours after their ferry’s departure time.
“I know there were a few irate people this morning,” he said.
“We all had visions of what had happened to the crew ships around the world when passengers had tested positive and were left stranded and not allowed off.
“That would be a nightmare. It’s not the most comfortable boat.”
Stena Line said the six crew members were “doing well” and were showing mild symptoms.
The company said an additional 15 people were isolating after being identified as “close contacts”.
“The welfare of our passengers and crew is paramount at this time,” it added.
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