The 20-year-old pulled off the biggest victory of his fledgling career in the second round, beating sixth seed Felix Auger-Aliassime, and was well placed against Russian 27th seed Khachanov after recovering from a slow start.
But Draper began to show discomfort early in the third set and, after dropping serve in the 11th game and consulting with the trainer, he called it a day trailing 6-3 4-6 6-5.
It was not immediately clear what the problem was but it appeared to be something at the top of his right leg and he took an off-court medical time-out earlier in the set.
Draper took time to settle into the match with Khachanov, a two-time grand slam quarter-finalist, much the better player in the first set.
The Russian had an early break in the second as well but Draper retrieved that and slowly began to make his power game tell.
He levelled the match with a break in the 10th game and all appeared rosy when he moved into a 3-0 lead in the third.
But Khachanov got the break back and it was at that point Draper headed off court to have his injury looked at.
Perhaps disrupted by the break, Khachanov then dropped serve again, and Draper served for the set at 5-3, but he was going for huge shots in an effort to shorten the points and back came the Russian once more.
After losing a fourth game in a row, Draper sat down on his chair and shook his head while he talked to the trainer before getting up and shaking his opponent’s hand.
While this will undoubtedly be a huge disappointment, this week has been another demonstration of Draper’s enormous potential and he will break into the top 50 for the first time at the end of the tournament.