De Minaur left the court for a medical timeout after losing the first-set tiebreak but played on with his left thigh heavily bandaged. He had to stop after winning the first game of the second set, leaving him trailing 7-6(3) 0-1.
"I don't feel great... I want to say sorry to all the amazing fans," said De Minaur at the trophy presentation.
"I didn't want to finish like this... hopefully see you next year," added the 27-year-old fifth seed.
Both semi-finals ended prematurely on Monday, as Hubert Hurkacz retired with an injury and Daniil Medvedev was disqualified for hitting a spectator with a ball.
Sixth-seeded Djokovic's win continued the Serbian's unbeaten record at the tournament with 34 straight victories and ensured the 39-year-old won a singles title for the 21st straight year.
"I'm really sorry for the way you had to finish today, and I really hope that you can recover quickly," Djokovic told De Minaur.
The two had gone toe to toe in the first set, targeting the baseline to pressure each other. De Minaur almost broke Djokovic in the fifth game, but the Serbian saved the break point with a full-stretch backhand down the sideline.
De Minaur held firm, but the 27-year-old's error count increased during the tiebreak to hand the first set to Djokovic.
An exhausted Djokovic also needed treatment during the break, and the 39-year-old was surprised when De Minaur signalled the end of the match.
"This year has been quite challenging for me, lots of ups and downs, physical and health issues," Djokovic said.
"So I just tried to find a good feeling on the court, and obviously I know that when I'm striking the ball well, I can still compete at the highest level."