Andy Butler will take charge of the senior squad during their absence, starting with training on Friday and then the FA Cup first round tie at FC United of Manchester on Saturday.
The Rovers squad did not come in direct contact with the positive case so are not required to self-isolate.
Moore, along with Jamie Smith and Paul Gerrard, are not showing any symptoms of the virus but are required to self-isolate based on medical guidance.
Rovers were informed at 7pm on Thursday of the contact with the positive case and by 7.30pm, Butler had been asked to take charge.
The move was part of a pre-agreed contingency plan that would see Butler step up if the manager was unavailable for whatever reason.
The club have been impressed with the 37-year-old’s work in charge of Doncaster Rovers Belles and feel the senior squad will be in good hands. Rovers have also stated that Butler will be supported with whatever he needs for the job over the coming fortnight.
AFC Wimbledon – who Rovers visited on Tuesday night – have confirmed a number of individuals in the first team group have tested positive for Covid-19.
The EFL and FA have been consulted on the protocols for such a situation and are satisfied with Rovers’ response.
FC United have also been made aware of the situation.
Butler will be in charge when Rovers host Wolverhampton Wanderers U21s in the Papa Johns Trophy on Tuesday.
It is likely that next Saturday’s League One clash with Oxford United will be postponed due to international call-ups.
Matt Smith has been named in the Wales squad and Josef Bursik the England U21s while Danny Amos are set to be called up for Northern Ireland U21s.
The decision on whether to postpone the trip to the Kassam Stadium would be in Rovers’ hands and given the situation they find themselves in - along with having players unavailable through injury - it is almost certain they would elect to do so.
Moore and his coaching staff would return in time to oversee the clash with Sunderland on November 21.