The Italian No.8 seed, who had won back-to-back grass titles during his Wimbledon preparations, said he was "heartbroken" to have to miss out. "The dream is over for this year but I will come back stronger."
The Spaniard showcased his trademark fighting spirit to overcome a tricky test from Francisco Cerundolo, advancing 6-4, 6-3, 3-6, 6-4 after three hours and 36 minutes.
Tsitsipas climbed back to No. 5 in the ATP Rankings after he captured his first grass-court title and ninth tour-level crown overall at the Mallorca Championships.
Second seed Rafael Nadal will play Argentina's world number 42 Francisco Cerundolo in the first round while young sensation Carlos Alcaraz will take on Germany's Jan-Lennard Struff.
The reigning Indian Wells champion Taylor Fritz added his second title of the season to his list of accolades after defeating Maxime Cressy 6-2, 6(4)-7, 7-6(4) in an all-American battle.
Amritraj remains the highest-ranked ATP singles player from India in ATP history (No. 16), and he captured the most titles by an Asian singles player (15) during his career.
It is a second tour-level final for Medvedev in as many weeks on the grass, after he appeared in the championship match at the Libema Open in 's-Hertogenbosch just six days ago.
Last week, Medvedev was in action at the Libema Open, where he marched to his second tour-level final on grass at the ATP 250 event. Meanwhile, Medvedev's rise comes after Novak Djokovic failed to defend his crown at the French Open.