According to a statement from the ministry, those with the virus are not being treated at the prisons although isolation wards have been set up inside the facility.
The prisoners in question were sent to the designated Covid-19 hospitals after receiving the test results.
Rwanda has 13 prisons with a population of about 74,000 inmates.
Reports by the Rwanda Correctional Services (RCS) indicate that all persons who visit inmates will have to use available hygienic installations of hand-washing and avoid shaking hands while greeting until further notice.
Since the government announced a temporary lockdown, prisons have since restricted families and friends from visiting inmates until further notice, while RCS immediately suspended income-generating activities undertaken by inmates.
During the lockdown, prisons also allowed relatives and friends to send money to inmates via mobile money using designated telephone lines so that they can buy whatever they want in the prisons canteens.
The lockdown has also seen prison wardens limited from making movements outside the prison facilities while on security duty.
Apart from visit restrictions at prisons, RCS regularly supervises hand-washing in prisons to ensure the hygiene of inmates, as one of the most effective measures to prevent the virus from spreading.