Zverev beat the top two players in consecutive matches to earn his second title at the ATP Finals.
Djokovic was hoping to draw level with Roger Federer on six season-ending championship titles.
World number two Medvedev will face either Novak Djokovic or Alexander Zverev in Sunday's final at the Pala Alpitour in Turin after breezing to victory over Norwegian Ruud.
Ruud has joined top-ranked Novak Djokovic, No 2 Daniil Medvedev and No 3 Alexander Zverev in the semi-finals of the elite season-ending event
ATP Finals 2021: Daniil Medvedev edges Alexander Zverev in thriller, Jannik Sinner beats Hubert Hurkacz
Sinner replaced fellow home hope Matteo Berrettini in the draw who pulled out due to abdominal injury.
Peng claimed earlier this month that former vice-premier Zhang Gaoli had assaulted her, the first time the #MeToo movement has struck at the top echelons of the ruling Communist Party.
ATP Finals: Novak Djokovic begins quest for sixth year-ending title with straight-sets win over Casper Ruud
Djokovic, looking to complete a remarkable year with a sixth Finals title after only just missing out on claiming all four Grand Slams, got off to a strong start against eighth-seed Ruud
Defending champion Daniil Medvedev triumphed 6-7 (5/7), 6-3, 6-4 over seventh seeded Hurkacz.
Recently crowned the season-ending world number one for a record seventh time, Djokovic just missed out on winning all four Grand Slams in a single year.
Djokovic famously came back from two sets to love down to beat Greece's Tsitsipas at the French Open final to win his second Roland Garros.
The 24-year-old Pole will be looking to go one better than his compatriot, 2012 finalist Jerzy Janowicz, in Paris.
It was a case of third time lucky for the Dutch-Croatian fifth seeds, who lost their first two finals, in Marseille and at the US Open, earlier in the year.
The Spaniard, who has never won the elite eight-man event, was beaten 3-6, 7-6 (7/4), 6-3 by in-form Russian Daniil Medvedev, who will play Dominic Thiem in Sunday's final.
ATP Finals 2020: Daniil Medvedev overcomes Rafael Nadal in thrilling semi-final, sets up title clash against Dominic Thiem
Nadal, who has never won the elite event in his illustrious career, faltered when serving for the match in the second set and was beaten 3-6, 7-6 (7/4), 6-3.
Novak Djokovic, five-time winner finishes second in Group Tokyo 2020 behind Medvedev and will play third-seed Dominic Thiem in the semi-finals on Saturday.
ATP Finals 2020: Nadal earns hard-fought win over Tsitsipas to reach semi-finals; Rublev downs Thiem in dead-rubber
Nadal, whose haul of 86 singles titles includes just one on indoor hard courts, is chasing the biggest prize missing from his resume at the eight-man elite event.
International travel to Australia is still tightly controlled and all overseas arrivals must quarantine for two weeks, while individual states also have their own COVID-19 restrictions.
ATP Finals 2020: Medvedev downs Djokovic to reach semi-finals; Zverev keeps hopes alive after beating Schwartzman
Daniil Medvedev secured a spot in the semifinals of the season-ending tournament by dominating five-time champion Novak Djokovic 6-3, 6-3 Wednesday for his second straight win of the group stage.