The Serb, who was returning from six months out with a right elbow injury, was clearly in pain as his hopes of a seventh Melbourne Park title were extinguished on Rod Laver Arena 7-6 (7/4), 7-5, 7-6 (7/3).
He was keen not to take away from the glasses-wearing Chung's huge achievement after the 21-year-old followed up his win over fourth seed Alexander Zverev in the last round.
"Congratulations. Amazing," said Djokovic, who also had an apparent hip or groin problem, screeching at times when stretching for the ball.
Djokovic said the injuries started troubling him at the end of the first set and a decision on where he goes from here would be made after talking with his medical team.
Chung's reward is a last-eight clash with unheralded American Tennys Sandgren, who upset Austrian fifth seed Dominic Thiem 6-2, 4-6, 7-6 (7/4), 6-7 (7/9).
The Korean, ranked 58, described Djokovic as "my idol".
"I can't believe this, dream's come true tonight."
Sandgren was also in a daze, becoming just the second man in the last 20 years since Frenchman Nicolas Escude to make the quarter-finals on his Australian Open debut.
For a composed Federer, it was business as normal.
The Swiss defending champion swatted aside one-time training partner Marton Fucsovics 6-4, 7-6 (7/3), 6-2 to make the last eight for an incredible 14th time.
He will now play fellow veteran Tomas Berdych, a semi- finalist in 2014 and 2015, who demolished Italy's Fabio Fognini 6-1, 6-4, 6-4.
"We have had some good ones over the years going back all the way to the Olympic Games in Athens in 2004," the 19-time Grand Slam champion said of the Czech.
Berdych, who is on his way back from back problems, lost to the five-time Australian Open champion in the third round last year and the odds are heavily stacked again him.
Of the 13 quarter-finals Federer has contested in Melbourne, he has won the lot.
- Running everywhere -
======================
World number one Simona Halep eased into the last eight 6-3, 6-2 over unseeded Naomi Osaka of Japan, delighted to be off court early after an epic and gruelling three-setter in the previous round.
While the win was easy, she continues to nurse a troublesome ankle that she rolled early in the tournament.
She will play either sixth seed Karolina Pliskova or fellow Czech Barbora Strycova, seeded 20.
Germany's Angelique Kerber is the only Grand Slam champion left among the women, and she was given a big fright as she chases her second Melbourne Park crown after beating Serena Williams in 2016.
After crushing Maria Sharapova in the last round, she came up against gritty Taiwanese veteran Hsieh Su-wei.
At one point Kerber was serving to stay in the match, but she bounced back to win 4-6, 7-5, 6-2.
The win set Kerber up with a clash against American Madison Keys, a semi-finalist in 2015 who has found a new lease of life under the guidance of former great Lindsay Davenport.
Seeded 17, she flattened French eighth seed Caroline Garcia 6-3, 6-2 in just 68 impressive minutes.
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