The George Hotel on Baxtergate has posted on social media today that its bar is shut after a member of staff tested positive for the disease.
It says the hotel will remain open.
The post said: "Unfortunately we’ve had it confirmed this morning that a member of the bar team has tested positive for Covid-19.
"Due to this the bar will be closed today for a deep clean to ensure everyone remains safe and other bar staff advised to get a test as a precaution.
"We understand these are worrying times for all and thank you for your continued support.
"The hotel will remain open throughout as all rooms are disinfected and deep cleaned after each guest and full PPE worn by the housekeeping team."
Meantime, pub and cafe Arch and Abbey on Skinner Street said it asked staff to self-isolate as a precautionary measure after a customer was tested for coronavirus.
It posted: "We had a customer in on Friday who has had a precautionary test which has thankfully come back negative.
"We asked all our staff that were working Friday to isolate until the customer's test came back.
"We thoroughly deep-cleaned the pub on Saturday which was the reason we were open so late.
"The staff that have been at work over the weekend had not been in contact with the customer or the staff that had been asked to isolate so were not at risk.
"Thankfully we were able to react quickly and we're glad it was a negative result but we would have closed to get everyone tested had it been necessary and we will do if it is necessary in the future."
Also today, the Coliseum Centre on Victoria Place has said it is closing as a precautionary measure to enable deep cleaning, despite having no confirmed cases.
It posted on social media: "As a precautionary measure and for the safety of our staff and customers we shall be closing this week to enable deep cleaning. Up to date we have no confirmed cases."
A string of Whitby businesses shut at the weekend amid a jump in cases in the borough.
Some closed because staff were showing coronavirus symptoms and others because workers had been in contact with people later diagnosed with the disease,
Several had not had staff or customers with positive coronavirus tests or symptoms but said they were shutting temporarily as a pro-active step.
As of Sunday afternoon, the number of confirmed coronavirus cases in the Scarborough borough since the outbreak began was 598.
That figure is 20 more than last Monday, when it was 578.