The Swiss defending champion was leading 6-1 5-2 in the last-four contest before his South Korean opponent succumbed to a painful blister on his foot.
Federer, who will now contest a record seventh Australian Open final, has paid tribute to Chung and admitted that he is disappointed that the semi-final could not go the distance.
"I thought the first set was normal," BBC Sport quotes Federer as saying. "I couldn't tell what was going on with my opponent.
"In the second set I felt he was getting slower. He's had a problem with the blister. It hurts - a lot. At some point it's too much and you make things worse.
"Clearly I'm happy to be in the final - but not like this. He's had such a wonderful tournament."
Federer will face Croatian sixth seed Marin Cilic in Sunday's final.