The Swiss great was leading 6-1, 5-2 when Chung called it quits with foot blisters, and he will now face Marin Cilic in his 30th Grand Slam final on Sunday.
Chung, the first South Korean man or woman to play in a semi-final at one of the four majors, was treated in a medical timeout for the left foot problem just two games earlier.
But it came as a big surprise when the 21-year-old walked to the net at 30-30 and trailing 2-5 after 62 minutes in the second set to throw in the towel.
He leads 2014 US Open champion Cilic 8-1 in their meetings.
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"This feels bitter-sweet. Obviously I'm incredibly happy to be in the finals, but not like this," Federer said of the abrupt ending.
"I would have preferred a normal end, yes. But I must admit, as well, you do take the faster matches whenever you can.
"There's enough wear and tear on the body, there's enough tough matches throughout the season that when they happen, you take them.
The Swiss maestro now has a 30-13 win-loss record in Grand Slam semi-finals and has yet to drop a set in this year's Australian Open.
"You couldn't tell until the end," he said of Chung's injury problems. "That's probably why a lot of people are stunned (he retired).
"I could tell something was wrong before he took the injury timeout, but he has a great composure.
"I think he is already a great player, but we are talking next level excellence and I think he will achieve that.
It was a muted semi-final with the retractable roof closed on Rod Laver Arena for rain, further improving Federer's chances given his strong indoor record.
He broke Chung's opening service and twice more to romp away with the first set in just 33 minutes as the Korean made a flurry of errors.
It got no better in the second set with Federer again breaking in the fourth game before the trainer was called on to the court to treat Chung for his foot blisters.
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Chung only lasted a bit more than two games before pulling out to a stunned silence.
"It's like worse than regular blisters. Over the last few days, it was blister under blister under blister," said Chung at his post-match press conference.
"Now it's red raw."
He added that retiring was the "right thing".
"If I play bad on the court, it's not good for the fans and audience as well," he said.
Federer was sympathetic.
"I've played with blisters in the past a lot, and it hurts a lot, and at one point it is just too much and you can't take it anymore," he said.
Federer broke Chung's serve four times off 11 break points and only had one break point on his own service.
The Swiss second seed hit 24 winners while Chung made 17 unforced errors in 14 games, eight of them off his normally potent forehand which Federer targeted.
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