Wildcard Fruhvirtova was leading 6-2, 3-0 when the 32-year-old Azarenka informed the chair umpire that she was done and left the court.
Kontaveit rallied from a set down to beat top-seeded Maria Sakkari in the final.
The Spanish great is now one major title clear of his ‘Big Three’ rivals after surviving the 2-6, 6-7(5), 6-4, 6-4, 7-5 thriller at Rod Laver Arena.
The world No. 1 ended Australia's 44-year wait for a home winner at the Australian Open by beating American Danielle Collins.
World No. 1 Barty's victory ended Australia's 44-year wait for a home winner since Chris O'Neil won the women's title in 1978.
Should Medvedev defeat the Spanish great, he will become the first man in the Open era to win his first two Grand Slam titles in succession after his triumph in New York last September.
A win for Nadal in Sunday's final will break a three-way tie with Novak Djokovic and Roger Federer and give him sole owenership of the record for most Grand Slam singles titles.
The top seed Barty defeated Madison Keys 6-1, 6-3 in the semifinals.
World No. 2, Medvedev beat Felix Auger-Aliassime 6-7(4) 3-6 7-6(2) 7-5 6-4.
Swiatek rallied from a set and a break down in brutal heat to overpower Estonian Kaia Kanepi 4-6, 7-6(2), 6-3.