Sinner told the crowd: “I’m super sorry to disappoint you. From yesterday I didn’t feel great, I thought I would improve but it came up worse.
“I tried to come out, to make it at least a small match, but I couldn’t handle more.
“I am very sorry for all of you. I know that maybe some of you, on a Monday, you had to work, had to do something else, so I’m really sorry.”
It is a first Cincinnati title for Alcaraz and a seventh triumph of the season overall – but as he said afterwards, this is not the way he would have wanted to win.
“I can’t say anything you don’t know already. You will come back even stronger like you always do,” Alcaraz said to Sinner.
“That’s what true champions do and you are one.”
Sinner, Alcaraz and women’s finalist Iga Swiatek are all due to play in the US Open mixed doubles on Tuesday in New York – but it seems unlikely Sinner will now pair up with Katerina Siniakova as planned.
The singles main draw at Flushing Meadows begins on Sunday.