Prime Minister Andrej Babis said he will meet with the country’s president later in the day to discuss a possible replacement for the minister, Roman Prymula.
“There’s no other solution than his resignation from the post,” Mr Babis said. “It shouldn’t have happened.”
“If we want the people to abide by the rules… it is us who have to set an example,” Mr Babis said.
“We can’t preach water and drink wine.”
The Blesk tabloid daily said Mr Prymula met with Jaroslav Faltynek, deputy head of the senior government ANO, or YES, movement led by Mr Babis in a Prague restaurant on Wednesday night.
Photographs published in the paper showed that Mr Prymula also did not wear a mandatory face mask.
Restaurants are closed in the Czech Republic because of the pandemic, and it was not immediately clear if the establishment was open or if the owner only allowed Mr Prymula and Mr Faltynek in to dine there.
The revelation has shocked the country, which has been hard-hit by the pandemic. At Mr Prymula’s request, the government has approved tight restrictions to slow the surge that is threatening the entire health system.
The junior government coalition party, the Social Democrats, joined the opposition to demand Mr Prymula’s resignation, calling his behaviour “absolutely unacceptable”.
Mr Prymula denied any wrongdoing and refused to step down, further escalating the crisis.
He said he was invited to participate in a meeting with a hospital director and only went through the restaurant to a private space where it took place.
“I haven’t broken anything,” he said.
Mr Faltynek apologized for the meeting and said he asked Mr Prymula to meet to discuss a special parliamentary session that is set to approve a plan for Nato military medical personnel to come to the Czech Republic to help their local colleagues.
Before he became health minister, Mr Prymula was a deputy health minister who led the government’s response to the coronavirus pandemic for a time in the spring.
The country recorded a relatively low number of Covid-19 cases and deaths then compared to hard-hit Western European countries such as Italy, Spain and the UK.
Mr Prymula, an epidemiologist, later assumed a different post, as a government health care envoy.
He was appointed only a month ago as a “crisis manager” to lead the country’s response to the pandemic as new infections were on a steep rise.
Mr Prymula became health minister on September 12, and he imposed a series of tough regulations in attempts to slow the steep rise of infections.
Bars, restaurants and schools are closed, as well as theatres, cinemas, zoos and many other locations. Professional sports competitions are banned.
Just hours before the incident in the restaurant, Mr Prymula and Mr Babis announced the country was returning to a lockdown like in the spring with new restrictions that limit movement, close many stores and services and limit public gatherings to two.