Speaking at a briefing on Tuesday, she said: "The pandemic situation is extremely severe now in Hungary. As in other European countries, we have to deal with ever-increasing figures in the healthcare system."
Central Europe is experiencing a third wave of infections.
"This increase has reached an extent that we haven't experienced so far, not even during the second wave of the pandemic," added Muller.
Last week, Prime Minister Viktor Orban said hospitalizations could rise to more than double their current level, but insisted the Hungarian health system could cope.
Other countries in the region have sent seriously ill patients to Germany for treatment, as their hospitals struggle with capacity.
New restrictions came into effect in Hungary earlier this week in an effort to bring the situation under control. Schools, shops and fitness centers were all forced to close, while a curfew remains in place from 8 p.m. to 5 a.m.. Masks are mandatory in all public places, including outdoors.
After technical glitches over the weekend hampered Hungary's vaccine roll-out, officials say the program is back on track. Five different vaccines are in use in the country, the highest number in the European Union, after regulators approved Russia's Sputnik V and China's Sinopharm jab. Authorities hope the inoculation drive will reverse the trend before Easter.
More than 1 million people – around 10 percent of Hungarians – have received the first dose of a vaccine. More than 300,000 have received both doses. Officials claim that by Wednesday, Hungary will be the most vaccinated country in the EU per capita.