Patients have been unable to get an appointment at a city surgery due to a large number of staff being off work.
St Stephens Gate Medical Practice in Wessex Street, located just off Chapelfield Road, has a reduced service for the rest of the week as well as next week.
A statement by the partners of the practice issued on Wednesday morning said: "Unfortunately we have a large number of staff away with Covid.
"Emergency appointments will still be seen. We will contact you if your appointment needs to be rescheduled."
Patients are urged not to call the practice to check on the status of their appointment.
The statement continues: "We would ask for your patience and understanding at this time. Thank you and we are sorry for any inconvenience."
County councillor Emma Corlett (Lab) who represents the Town Close division, said she had two patients contact her about the limited service on Wednesday morning.
Ms Corlett added: "This news is hardly surprising and it is no wonder the system is at breaking point.
"I wish the staff well and hope they recover soon."
Ms Corlett currently has Covid and was admitted to A&E earlier this week.
She added there are others with health vulnerabilities who are currently "being thrown to the wolves".
She continued: "I am 46, fit and healthy, triple vaccinated with no underlying conditions but other people are not so lucky.
"This isn't a local system issue. This is a result of the reckless decision by the government to remove basic protections."
The government has said vaccines remain the best defence against Covid with spring boosters now being offered to the elderly, care home residents and the most vulnerable.
Secretary of State for Health and Social Care Sajid Javid said: "Thanks to our plan to tackle Covid we are leading the way in learning to live with the virus."
It comes after new guidance is set to be outlined by government urging people who have a cough or cold are to be urged to “stay home and avoid contact with other people”.
The advice is set to be issued on April 1.
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules here