At least four inmates have tested positive and many more are quarantined in Ndolo prison in the capital city, Kinshasa.
The overcrowded prison is hosting inmates at nearly four times its capacity.
Human rights organisations are concerned the virus could easily spread among prisoners and to the relatives who visit them.
Rights groups are asking for the release of prisoners accused or convicted of petty crimes to ease overcrowding.
Health officials have dispatched a team to the prison to investigate the outbreak.
DR Congo has confirmed cases of the new coronavirus in at least seven provinces, but the majority of the cases have been concentrated in Kinshasa.
The eastern part of the country, which has no active cases at the moment, has today reopened travel between cities in those provinces.