The opposition is furious at the decision, which is seen as a way to put the lid on it.
But enough has already surfaced to spark speculation about new elections in Austria.
- It is difficult to say whether mere allegations of corruption in themselves can lead to the dissolution of a government in Austria.
Unfortunately, Austrians have a surprisingly high tolerance for corruption, says Mathias Huter who is an anti-corruption activist at an organization in Vienna.
"Bad starting point for new elections"
Whether there will be a new election or not depends on two things.
Partly on whether the bribery suspicions lead to prosecution.
And how the Green Party, which rules together with Kurz liberal-conservative ÖVP, in that case stands.
The Green Party, on the one hand, has had difficulty defending its partner, but on the other hand has so far not opened up to leave the co-operation.
Sebastian Kurz's party is shaken by several scandals.
Among other things, his finance minister is to be suspected of bribery.
Part of the evidence is secret video recording.
Photo: JOHANNA GERON / POOL / AFP
- The Greens would have a very bad starting position in a new election.
They have probably lost some support.
Some of the promises they have made about climate policy and anti-corruption have not yet been delivered.
Therefore, they have no great interest in new elections right now, says Huter.
Police searched houses
Finance Minister Gernot Blümel had his house searched by police in February to secure any evidence.
An SMS to him from the CEO of a large casino company directed the suspicions against him.
The casino CEO asked where Blümel and Kurz for help in a tax dispute the company ended up with Italy.
In the same SMS, the CEO wrote that he also had a donation to give to the party.
It is not established whether Kurz was reached by the content of the message.
Blümel denies that the party received money from the casino.
Secret video recording
Prosecutors in Vienna became suspicious of the casino company Novomatic after the company's name was mentioned in a high-profile secret video recording from Ibiza that overthrew Sebastian Kurz's previous government in Austria.
-Novomatic pays everyone, the country's former deputy chancellor Heinz-Christian Strache, from the right-wing nationalist FPÖ, was heard saying in the film.
The company's CEO himself denies bribery.