The Swiss legend, seeded 17 after his 2016 season was cut short by a knee injury, was expected to meet five-time runner-up Andy Murray after overcoming world number five Kei Nishikori in the round of 16.
Instead Federer will take on the 50th-ranked, net-rushing German left-hander Zverev, who stunned Murray in the fourth round, as he pursues a fifth Australian crown at age 35.
The victor will play the winner of Tuesday's other quarterfinal, between 2014 champion Stan Wawrinka and former finalist Jo-Wilfried Tsonga, for a place in the final.
Zverev, elder brother of rising German teen Alexander, shocked world number one Murray with an assiduously executed serve-volley game that kept the Scot out of his comfort zone.
Zverev will again strive to keep the rallies short and spend as much time at the net as possible, but his challenge will be to attack Federer's stronger second serve.
The 29-year-old German journeyman didn't win a game in his last meeting with Federer at Halle in 2013, and lost their other encounter in straight sets in Rome four years earlier.
But Federer is wary of taking on the rejuvenated Zverev in the unique pressures of a best-of-five-set quarterfinal on the slick Rod Laver Arena hardcourt, where Murray and six-time winner Novak Djokovic have been ambushed in this year's tournament.
'Playing Roger will be a dream'
“Obviously he's on a high right now. He's feeling great. Probably feels the best he's ever felt on a tennis court,” Federer said.
“It's going to be tough and different and tricky. That's my mindset.
“Of course I'm the big favourite in this match, but I prefer to be the favourite. I did it for years and years. It makes me feel comfortable.”
For Zverev, it will be a “dream” match with Federer.
“Playing Roger will be a dream for me. Growing up I was inspired by him. He's my favourite player,” he said, after taking out Murray in four sets.
Seasoned pair Wawrinka and Tsonga will also look to cash in on the absence of Murray from their side of the draw as they aim for a semifinal place.
Wawrinka, as a three-time Grand Slam champion, including a 2014 Melbourne final win over Rafael Nadal, will be the favourite.
The Swiss world number four leads the 12th-ranked Frenchman 4-3 and has won their last three meetings. He beat Martin Klizan, Steve Johnson, Viktor Troicki and Andreas Seppi to get to the last eight.
“Tsonga has always been around the top 10. He was number five in the world. He made the final here. It's going to be an interesting match,” Wawrinka said.
Tsonga, the 2008 finalist who battled past Englishman Dan Evans over four sets in the fourth round, said he will be ready to take on the Swiss.
“It's going to be a tough match. I know he's playing really good. It's going to be important for me to play my best level. I think I will be ready,” he said.