Sinner had upset world number one Carlos Alcaraz (19) in Friday's semi-final but he struggled in the heat against the fourth seed Medvedev, who triumphed 7-5, 6-3.
The win was Medvedev's 19th career ATP title and his fifth in a Masters 1000 event and confirmed his dominance on hard courts in 2023.
Sinner, also beaten in the Miami final two years ago and now with a 0-6 record against the Russian, said he had not been at 100%.
"We woke up this morning, not at my best, I felt a little bit sick... unfortunately, today I couldn't play at my best," said the Italian who, however, said there had been no question of him pulling out of the contest.
"No, it was not that bad. But, you know, with the heat, when you run a lot, it gets a little bit worse and worse. Obviously the first half an hour we played in the sun also," he said.
Medvedev said he was fortunate that Sinner had to come through a physical, three-set battle on Friday night against top seed Alcaraz.
"I think everyone enjoyed the semi-final against Carlos, it was amazing," Medvedev said at the trophy ceremony, where he collected nearly $1.3 million in prize money.
"I'm probably a little bit lucky because at that point I was already in bed watching you run all over the place, both of you. I know it is not easy to recover after such a match."
Medvedev, who called himself a "hardcourt specialist" when loudly complaining about the slow speed of the courts in Indian Wells, said he was grateful for the faster surfaces in Miami.
"I can handle myself and be calm on the court when I feel like it is a real hardcourt," he said with a smile.
"I don't know who makes these decisions but thanks a lot to everyone who made this court this year. I was really happy to play on it."
The tour now moves to the clay court season, a surface on which Medvedev has not enjoyed his best form.
"Now clay season starts so let's see how you do there," Sinner said with a smile. "But I wish you all the best."
The Russian, who had already won titles at Rotterdam, Doha and Dubai, started confidently, holding serve to love while Sinner's first service game was a real battle.
Sinner had to save a break point and fought through a 26-shot rally before coming through at the end of a 10-minute game.
In contrast, Medvedev again served to love but Sinner was showing signs of settling as he held his serve and then the Italian broke Medvedev to go 3-2 up, with a deft touch volley.
Medvedev immediately broke back, however, with Sinner's effort clipping the net and going out and after the Russian held again, the Italian had attention from the ATP trainer.
Sinner, looking uncomfortable in the bright sunshine, took a pill along with a powder in his water in the 30.5 degrees (C) heat.
Medvedev, looking composed and confident, grabbed the first set when Sinner was serving at 6-5 down and the Italian's poor shot into the net handed the Russian the crucial break.
Medvedev quickly got ahead in the second set when Sinner sent a forehand long but just as quickly handed the break back to Sinner.
But Sinner was making too many errors and when Medvedev broke again to go 3-1 up, the Italian was unable to turn things around and the world number five coolly completed his first-ever win in Miami.
