Concerns have also been raised that ferry provider Northlink Ferries are putting passengers at risk by continuing to serve food on board.
The operator has ceased the cinema and car valet services and closed the the shops, bar area and bed and breakfast facilities onboard the MV Hamnavoe.
However, passengers on board crossings from Aberdeen to Lerwick and Kirkwall will still have access to food and drink and are allowed to move around on board.
A concerned relative of a Northlink staff member said the company are “putting revenue before people’s lives” by carrying on like “business as usual”.
He explained: “They are just not taking it seriously. This is a highly contagious virus and it’s just bizarre their behaviour.
“They could easily shut down, confine people to cabins and they haven’t . They are still allowing people to roam around the vessel, touching banisters as they are going up and down the stairs.”
Serco’s Managing Director of NorthLink Ferries, Stuart Garrett, said: “Whilst we do continue to provide a lifeline service we would like to remind all passengers to adhere to Government guidelines when travelling with us for the safety of themselves, their families and our staff.”