Musetti, the fifth seed, took little more than two hours to beat ninth-seeded American Fritz 6-2 7-5 6-4 at Rod Laver Arena on Monday.
It came as two-time defending champion Jannik Sinner beat fellow Italian Luciano Darderi 6-1 6-3 7-6 (7-2), booking a quarter-final date with Ben Shelton..
The big-serving American came from a set down to beat Norway's Casper Ruud 3-6 6-4 6-3 6-4.
Musetti produced a dominant performance against Fritz, moving well despite going through a tough five-set battle with Tomas Machac in the previous round.
Fritz, meanwhile, struggled with a knee injury that has bothered him for months and was also limited by an oblique muscle issue that could force a stint on the sidelines.
Musetti has reached the semi-finals at Wimbledon and Roland Garros, as well as the US Open last eight, but had never previously been past the third round at Melbourne Park.
The 23-year-old's first foray into the second week has come despite his coach Simone Tartarini and physio Damiano Fiorucci both returning to Italy for personal reasons.
"They are here with the heart," Musetti said on-court after his latest victory.
"It's tough also to speak because when real life knocks the door it's something really surprising.
"You always understand life better and I think I feel more mature on the court.
"I'm probably playing better also for that. I want to continue and I want to keep pushing myself more and more.
"Now I have a huge challenge ahead. I feel ready to do it."
Musetti has only once beaten Djokovic in 10 previous attempts and faces a difficult assignment against the 24-time major winner.
The Serb will be refreshed after he was granted easy passage to the quarter-finals when his fourth-round opponent Jakub Mensik pulled out injured.
But Musetti is buoyed by his strong performance against Fritz, in which he broke the American's big serve twice in the opening set and took control late in the second, when he won three straight games.
Musetti broke again early in the third set to heap pressure on his opponent, and moved Fritz all over the court.
"Trying to use my variation to lead the game, like today with the forehand, and try to open the court and try to make the opponent move," Musetti said.
"Before I was starting to play a little bit too far and then I was a little bit passive on the rally.
"Now I think a little bit more energetic and aggressive, and my coach always keeps telling me to be a little bit more aggressive and go for it to try to take the lead of the rally.
"That's what I have done today, so I'm really, really happy."
Fritz has battled knee tendonitis for months but felt strong on Monday morning, only for the issue to flare up again during his pre-match preparation.
The 28-year-old had not previously revealed the oblique injury, but said it was "killing me" during a third-round win over Stan Warwrinka.
Fritz had strapping around his torso for the Musetti clash, but removed it midway through the match.
"It's the exact same thing I had last year that took me out for the beginning of clay court season and a bit during the hard court season I tried to play through," Fritz said.
"All the scans show that there's not like an obvious tear there like there was before.
"But, you know, I'm being cautious, because it's all the same symptoms ... same shots hurt me."
Fritz is hopeful of playing next month's Dallas Open but is prepared to take time out if required.
"I'm not going to have to play more than three sets any match in Dallas, so I'll figure it out" he said.
"If my knee feels like it's not getting better, if my oblique feels like it's not getting better, I'll give myself the time."
