Venko Filipce made the announcement shortly after his deputy minister and two senior hospital administrators also stepped down.
There was no immediate reaction from the office of Prime Minister Zoran Zaev.
The fire broke out late Wednesday in the western town of Tetovo, destroying the facility within a few minutes. Twelve people were also injured. The blaze is believed to have started by accident, although an investigation is still under way. Witnesses and officials have said an explosion preceded the fire.
The public prosecutor’s office said eight women and six men aged between 29 and 78 were killed.
North Macedonia has said it is accepting an offer from other NATO allies to send fire experts. The government announced that a team from Germany’s Federal Criminal Police Office will join the investigation.
President Stevo Pendarovski has said the investigation would be completed within five days, and that indications are the fire was not set deliberately.
“It all lasted three to five minutes,” said Gzim Nuredini, head of Tetovo’s COVID-19 center, adding that medical staff and patients’ relatives who were outside all tried to help extinguish the flames.
Prosecutors from Tetovo and the capital, Skopje, were gathering video material from inside and around the hospital, and have hired an electrical engineering expert to help determine how the blaze broke out.
Medical staff and witnesses have also been questioned, and prosecutors have ordered the confiscation of all documentation on the construction of the facility to check for potential omissions.
North Macedonia’s government has declared three days of mourning from Thursday.
Fires in COVID-19 hospitals or wards have cost dozens of lives in other countries, including Iraq and Romania.