Passengers arriving at the airport have been required to present a health certificate showing a negative COVID-19 result which is no older than four days, or go into quarantine.
From Monday passengers can have a molecular biological (polymerise chain reaction or PCR) COVID-19 test at the airport, and get the result in two to three hours, the airport said.
"Air travel, whether business journeys or urgent trips...will thus become safer and easier," it added on Sunday.
Last month Emirates, in coordination with Dubai Health Authority (DHA), said it was the first airline to conduct on-site rapid COVID-19 tests for passengers.
Austrian quarantines that have already begun can be ended if the person is found to be clear of COVID-19, Vienna Airport said.
The airport tests, which cost 190 euros ($209), can also be taken by passengers leaving Vienna to demonstrate their virus-free status at their destination.
Vienna Airport is operating scheduled flights to Doha, Dortmund, Duesseldorf, Frankfurt, Hamburg, Lisbon, Minsk and Sofia, as well as charter flights and business trips. It has landing bans in force from flights from high risk areas.
Austria has recorded 15,526 cases of the new coronavirus, and 598 deaths. It has started to loosen its seven-week lockdown, with shopping centres, larger shops and service providers including hairdressers reopening last week.