No29 seed Korda needed a medical timeout in the second set for treatment but was not able to improve the issue and pulled out when behind 7-6, 6-3, 3-0.
The extent of the problem is unclear but the 22-year-old, son of the former Australian Open champion Petr, faces a potentially lengthy spell on the sidelines.
After the walkover, Russian Khachanov said: “Back-to-back semi-finals in a Grand Slam feels great. Obviously, not the way you want to finish the match. I think until a certain point, it was very competitive, a very good battle.
“Sebastian beat one of the my friends, Daniil Medvedev in three sets and won in five sets against Hurkacz. He is playing great tennis.”
Earlier, Wimbledon champion Elena Rybakina made light work on despatching Jelena Ostapenko 6-2, 6-4.
The 23-year-old Rybakina has struggled since winning her first Grand Slam title but looks to have returned to her best form at Melbourne Park.
Rybakina had lost both her previous career meetings against Ostapenko but needed just an hour and 19 minutes to ease her way into a second career Grand Slam semi-final.
Following the win, she said: “I got all the experience at Wimbledon and it’s helping me now this time here in Australia, and I know what to expect. I’m feeling good on the court and just really enjoying every match I’m playing here.”