Kurz, a Catholic, also announced the news on Twitter April 21, alongside other measures to ease the lockdown in Austria.
"It is good that we can go the way of reopening and there is also light at the end of the tunnel for the economic development of our country," he tweeted.
"Our motto for the next phase is clear: as much freedom as possible, as much restriction as necessary."
A statement on the website of the Federal Chancellery of Austria said that church services will be permitted "subject to certain conditions and safety regulations to protect health".
The statement added that Susanne Raab, the country's minister of education and cultural affairs, will share further details, in consultation with religious communities, on Thursday, April 23.
Responding to the news, Cardinal Christoph Schönborn of Vienna tweeted: "We will soon be able to celebrate the Eucharist together with great joy and responsibility."
He added: "Faith needs both: the celebration together and the personal relationship with God. This is where Christianity comes from. The community of the Church is something essentially different from a club or a group of friends."
Austria, which has a population of 8.9 million, was one of the first European countries to enter lockdown. The first two cases of coronavirus were confirmed on February 25. From March 16 onwards, Austrians were ordered not to leave their homes except for reasons such as essential work or shopping.
Almost 15,000 people have contracted COVID-19 in Austria and 491 people have died as of April 21, according to Johns Hopkins University Coronavirus Resource Center.