The new measures would apply to unvaccinated members of the public, Alexander Schallenberg added.
It follows a meeting on Friday evening between Mr Schallenberg and state-level leaders to discuss their response to rapidly increasing cases.
“The pandemic is not yet in the rear-view mirror,” Mr Schallenberg said. “We are about to stumble into a pandemic of the unvaccinated.”
Austria reported 20,408 new cases of Covid in the latest seven-day period, according to health authorities, bringing the seven-day average to 228.5 cases per 100,000 people. A week earlier, that figure was at 152.5.
Mr Schallenberg also announced that if the number of Covid patients in intensive care units (ICU) reaches 500, or 25 per cent of the country's total ICU capacity, entry into businesses such as restaurants and hotels will be limited to those who are vaccinated or recovered from the virus.
If the number reaches 600, he said, the government plans to impose further restrictions on unvaccinated people – in this case, they would only be allowed to leave their homes for specific reasons.
Currently, the number of Covid-19 patients in Austria’s ICUs stands at 220.
While the EU member’s government has encouraged its citizens to get vaccinated, the effort has slowed in recent months. A little more than 65 per cent of the total population has received one dose of the vaccine, while just 62.2 per cent are fully vaccinated, the latest figures show.
Additional reporting by Associated Press