Medvedev, who was seeded second behind top-ranked Novak Djokovic at the ATP Masters 1000 event on clay, has been put in isolation and is being monitored, the men's tennis governing body said in a statement.
"My focus is now on recovery and I look forward to getting back out on Tour as soon and as safely as possible."
Bautista will play for a place in the final against 19-year-old Italian Jannick Sinner, the world No. 31 who beat Kazakhstan's Alexander Bublik 7-6 (7/5), 6-4.
In other men's action, John Isner, the 2018 champion and 2019 runner-up, booked a fourth-round spot with a 7-6 (7/5), 7-6 (7/5) victory over 11th-seeded Canadian Felix Auger-Aliassime.
The relentless Russian will contest his first final at Melbourne Park on Sunday and look to claim his maiden Grand Slam title after beating Tsitsipas 6-4 6-2 7-5 at a floodlit Rod Laver Arena.
Yet Medvedev has now won 20 successive matches and 12 against top-10 opponents, including beating Djokovic on the way to winning the ATP Finals.
Fourth seed Medvedev served like a machine until broken in the third set, which revived the Greek fans in the terraces as Tsitsipas roared to a 5-4 lead.
"I'm happy to manage to keep my nerves because still I didn't make so many bad shots," Medvedev said on court of his anxious third set.
Medvedev, who lost the only previous encounter between the two players, at Indian Wells in 2019.
Medvedev had never won a five-set match in six previous attempts, but after breaking the Serbian for 2-0 in the decider with a crunching forehand winner.
The fourth seed blew a two-set lead and needed treatment to his left glute before finally moving past the Serb 6-3, 6-3, 4-6, 3-6, 6-0 and into the fourth round, extending his win streak to 17.
"It's tough to say because it can both be negative and positive," said the Russian, whose best Slam performance so far was making the final of the 2019 US Open.