A man sitting in the stands behind Medvedev's side of the court was seen holding his face and escorted out of his seat after being hit, as Djokovic was serving for the match with the score at 7-5, 5-3.
Eleventh-ranked Djokovic will play world number nine Alex de Minaur for the title on Tuesday in Beijing.
The Australian had advanced over Hubert Hurkacz after the 29-year-old from Poland retired from their semi-final with an abductor strain.
Medvedev hit the ball with a backhand at the edge of the stands when he failed to return a point, with the chair umpire stopping play.
"Terribly sorry to the spectator, first of all," he told reporters afterwards, adding it was "100% an accident" and that he wished to apologise to the fan in person.
"The ball was bouncing back, so I tried to, like, just hit it anywhere, so it doesn't go out from the court," he said.
It had been a physical battle before Medvedev's disqualification.
Djokovic was red-faced and hunched over between points, with both players forcing each other through gruelling rallies, until the Serbian took control in the second set.
A valiant Djokovic, 39, put on a dazzling performance and saved 16 break points across the match, diving at the baseline and sprinting to the net.
"I didn't see what happened, to be honest," he told the crowd after the fan was hit.
"I'm sure that Daniil didn't... do it intentionally. It happened by accident. Sorry for the crowd," he said, adding that it had been a tough match.
"I know the feeling," Djokovic told reporters later, recounting his own disqualification from the 2020 US Open after accidentally hitting a ball at a line judge.
"It's horrible... but it happens," he said.
Although Djokovic was three points away from winning the match, he said victory wouldn't have come easy and that he got "lucky" in a "very exhausting" battle.