Four other unnamed sites were fined for various offenses, including transactions after the 10 p.m. curfew.
They are just the latest in a series of places required to close by the council. Five sites slated to close last week have all reopened since.
Joanne Waller, chief of community protection services for Durham County Council, said officers would continue to conduct spot checks at premises in the area.
She said: ‘Meeting the latest restrictions is something all county venues are legally required to do and failure to do so could result in a £ 1,000 fine or closure, depending on the severity of the violation.
“As the county remains on High Alert Level Two, it is essential that we all do our part to protect each other from the coronavirus and save lives by following the law and adhering to public health guidelines.
“I understand that the vast majority of locals are compliant and have health protection measures in place, but it is essential that every site does this and we will continue to act until we are satisfied that the appropriate measures are in place everywhere. ”
The closures come as the Northeast is once again on the brink of tighter restrictions.
Although coronavirus cases fall in the majority of zip codes, an explosive email warned local leaders the region could still be placed at level three.
The three Durham sites that have been ordered to shut down must do so for at least a week, or until they can assure the board they can operate safely against coronaviruses.
Current rules mean that venues must provide table service only, close at 10 p.m., have the necessary tracking and traceability requirements, ensure social distancing rules are followed, and require staff and customers to wear masks.
The public is prohibited from mingling indoors with anyone who is not part of their household.
Amanda Healy, County Durham Public Health Director, said: “We know the majority of locals and people in County Durham are acting responsibly and we are grateful for that.
“However, as long as we face a high risk of coronavirus, we must all work together to keep up with the latest restrictions, reduce the spread of the virus and save lives.
“Following the latest public health advice will also help keep people safe.
“Residents must therefore wash their hands often and for 20 seconds, cover their faces in public, stay two meters from each other and stay at home if they show symptoms of coronavirus or wait for the results. of their rest. “