A spokesman for the hospital said those who had been in contact with the patient had been given emergency contact details in case they develop symptoms and advice about self-isolation.
There are now 60 confirmed cases of coronavirus in Nottinghamshire and 5.683 across the country.
So far 281 people have died in the UK.
Dr Tim Noble, Medical Director at Doncaster and Bassetlaw Teaching Hospitals (DBTH), moved to reassure the public precautions were place to minimise the risk of further infection.
He said: “As a Trust we have put the necessary precautions and safeguards in place and our clinicians are working to national guidance to ensure they are compliant with infection prevention and control measures to minimise any associated risks.
"Earlier this week we restricted our visiting hours and we have started to significantly scale back outpatient and elective appointments and procedures.
“Patients who require urgent and emergency care should still use appropriate services.
"The best advice for our local residents is to wash your hands regularly with soap and water, avoid touching your eyes, nose or mouth and use and discard tissues if you cough or sneeze.
“Also I would urge everyone to follow social distancing advice when at home and stress the importance of this to friends and family.
“These are the best steps that we can all take to help reduce the spread of Covid-19."