The Communications Workers' Union said it was highly unlikely any mail will be delivered in the city on Tuesday
Royal Mail staff in Londonderry have refused to enter the city's sorting office until a deep clean of the premises is carried out.
More than 40 staff - a third of its 120-strong workforce - are off work because of Covid-19, the Communication Workers' Union (CWU) said.
The union said 17 staff at the office have tested positive, with 13 of those having been diagnosed since Friday.
A further 25 members of staff are self-isolating, it added.
The CWU's Charlie Kelly said it is a "scary time for staff".
He said it is "highly unlikely" there will be a postal service in the city on Tuesday.
"Staff want a commitment as to when it (the deep clean) is going to get done," he said.
Rise in cases
"Until we get that commitment they say they are not going back into the building because they feel their health and safety is under threat."
Staff and management are due to hold talks later on Tuesday morning.
There has been a sharp rise of confirmed cases over recent weeks in Northern Ireland's north west region.
There have been 4,292 confirmed cases in the Derry and Strabane council area since March - 1,160 of them were diagnosed in the past seven days.
BBC News NI have asked Royal Mail for comment.
Royal Mail has previously warned postal services could be disrupted in some areas due to absences but that measures are in place to protect staff.
"As well as encouraging good hand hygiene, standard ways of working have been revised to ensure that colleagues maintain appropriate social distancing at all times," a spokesperson said.