Footage shared on social media showed a building in flames and a thick cloud of black smoke billowing into the air near a main road in the city of Tetovo.
Firefighters reportedly extinguished the blaze less than an hour after it broke out at about 21:00 local time (19:00 GMT) on Wednesday.
Health Minister Venko Filipce warned the number of casualties could rise.
“This is a very sad day,” he wrote on Twitter, adding that several patients had been “urgently transported” to a hospital in the capital Skopje.
“Doctors are fighting for the lives of the injured,” Mr Filipce said. He described the fire as a “terrible accident”, but provided no further details.
It is unclear how many patients were being treated at the centre in Tetovo when the incident occurred.
The temporary facility was reportedly constructed last year to care for people made seriously ill from the coronavirus.
North Macedonia has a population of about two million people.
The country has reported more than 180,000 cases of Covid-19 and 6,153 coronavirus-related deaths since the start of the pandemic, according to Johns Hopkins University data.