Djokovic advanced at 4-6, 7-6 (6). He will play third-seeded Stefanos Tsitsipas in Sunday’s final.
“I really hope that his injury is nothing too serious,” Djokovic said. “I know Daniil, he’s a great guy, he’s a fighter, he’s a big competitor. . . . He told me that he pulled an adductor muscle in his leg.
“It was such a close match, particularly in the second set. I would probably say he was a better player on the court in both sets. I was fighting and trying to find a way. I found a way to win the second, but I’m just sad for the tournament and for these people who were enjoying the battle, and for Daniil that it had to end this way.”
Going in to the match, Medvedev had a 4-6 win-loss record against Djokovic, and they hadn’t met since last November in the Paris final, where Djokovic won in three sets.
In the other semifinal, Tsitsipas rallied to beat fifth-seeded Andrey Rublev 4-6, 6-4, 6-3.
Rublev won the first set after saving three break points. Tsitsipas broke in the 10th game of the second to level the set score. He was more aggressive the longer the match went, and far more decisive than Rublev in the decider.
“My mentality kind of changed,” Tsitsipas said. “I played with more of an aggressive game style and didn’t have anything by luck. I was conscious of every single decision I was trying to follow and execute and those service games worked out pretty well. They kept me in the game and gave me that hope.”
He will be going for his third title of the year, after Monte Carlo and Mallorca, in his sixth final of the season.