World number one Sinner came into the final feeling poorly and lost the first seven points of the match played in 30 degrees Celsius summer heat.
Alcaraz is the third Spaniard to win the pre-US Open title here after Carlos Moya and Rafael Nadal.
Sinner will now focus on recovery with the US Open starting on Sunday.
The Italian is due to take part in the US Open’s revamped mixed doubles on Tuesday, but his participation in that draw is now in doubt.
“I’m super-super sorry to disappoint you,” Sinner said at the trophy ceremony to fans. “I was not feeling great yesterday but I thought it would go away overnight. I tried to make it at least a small match but I could not handle more.”
The defending champion, who turned 24 last Saturday, added: “Some of you (fans) had to (miss) work or do other things today, so I’m really sorry.
“I’m sorry to disappoint. Congrats to Carlos, I know this is not how you wanted to win. You are having an amazing season.
“I’m sorry to disappoint but sometimes it’s like this. This has been one of the hottest tournaments we have played.”
Sinner lasted for just 22 minutes, calling for the doctor after losing the fifth game and shortly after going to shake hands with Alcaraz.
It was the second match in a row he had won over an ailing opponent, with Alexander Zverev playing ill in the closing stages of their semi-final.
Alcaraz won his 22nd career title as he claimed his 17th victory in a row at the Masters 1000 level.
“This is not the way I want to win trophies,” Alcaraz said. I understand how Jannik is feeling right now.”
He called the Italian “a true champion, I know you will come back better and stronger than ever.” (AFP)