De Minaur has experienced a dream week in his home city and dominated the opening set of the final on Saturday, but 21 year-old Russian Medvedev battled back to triumph 1-6 6-4 7-5.
Medvedev struggled in the opening set with the crowd firmly behind De Minaur, yet he put an uncertain start behind him to win a thrilling battle at Ken Rosewall Arena, where Angelique Kerber earlier defeated another Australian, Ash Barty, in the women's final.
De Minaur, 18, had won 11 of his previous 12 matches in a superb start to the season and rallied from 4-1 down in the final set before qualifier Medvedev denied him the biggest moment of his fledgling career two days before the Australian Open begins.
Medvedev was blown away in the opening set, a vibrant 167-ranked De Minaur - the youngest ATP World Tour finalist since 2016 - handling the pressure impressively, breaking three times to leave his opponent startled.
World number 84 Medvedev looked far more composed in the second, gaining his reward with the only break and taking a tense battle into a final set when De Minaur was unable to return a powerful serve.
The momentum was firmly with Medvedev, who charged into a 4-0 lead as De Minaur tightened up, but the teenager was not finished yet, saving a match point prior to getting back on serve at 5-5, as the pair continued to trade punches.
Medvedev put the psychological blow of failing to serve out the match behind him, breaking straight back and this time serving out the match to love.