The venue will be decided at a later date as Austria return to Wales for the first time since losing a World Cup qualifier 1-0 in Cardiff in September 2017.
"The Football Association of Wales is pleased to announce that the men's national team will play an international friendly against Austria on Friday, 27 March 2020," said an FAW statement.
"This will be Cymru's first preparation match of the year ahead of the Euro 2020 finals in June where they will face Switzerland, Turkey and Italy in Group A."
Ryan Giggs' side booked their place at Euro 2020 – only Wales' third major tournament in their history – by winning back-to-back games against Azerbaijan and Hungary last month to finish second behind Croatia in their qualifying group.
An FAW delegation is currently in Azerbaijan, where Wales will meet Switzerland and Turkey in their first two games of Euro 2020 before they play Italy in Rome.
The FAW are looking at potential training bases in the capital Baku ahead of their opening game in the pan-European tournament on June 13.
Austria are in Group C at Euro 2020 alongside Holland, Ukraine and one of the as yet undetermined play-off winners.