So far it was planned by the Austrian side to lift the corona-based border barriers only in mid-June (15.6). But now since midnight the Austrian side has opened its borders to the neighbouring countries except Italy.
The Italian state consumer protection agency has even taken Austria to court because Italy, for its part, has opened its borders to Austria and now feels disadvantaged if Austria does not comply with the EU treaties on the free movement of persons.
Entry from the popular holiday destination of Croatia, also in June, still remains linked to a quarantine obligation by Austrian authorities, unless travellers can provide negative corona test results.
Even if Austria has opened its borders to the neighbouring states, some of its western neighbours have not relaxed their entry requirements for the time being. The complete freedom of entry to Germany, Switzerland and Liechtenstein will therefore, as previously planned, only apply from June 15th, as these neighbouring countries are maintaining their entry restrictions due to the coronavirus.
Details of the regulations of individual countries can be found under the following links of the Austrian Chamber of Commerce:
The opening towards the East has already taken place: Slovenia, Hungary, the Czech Republic as well as Slovakia followed suit after Austria's opening yesterday midnight, today on Friday (5 June 2020). Neither corona tests nor quarantine are required for travel to the four countries.
Please note, however, that there are still formal requirements (embassy note) for transit journeys, e.g. to Poland through the Czech Republic. The best thing to do before a transit journey is to visit the website of the Austrian Foreign Ministry and check the respective websites of the transit countries for current requirements.