Ailing world number one Sinner threw in the towel after Alcaraz roared into a 5-0 first set lead.
Italian ace Sinner said in an on-court interview afterwards he had started feeling ill on Sunday and his condition worsened overnight.
"I'm super super sorry to disappoint you," Sinner told fans. "From yesterday I didn't feel great. I thought that I would improve during the night but it got worse.
"I tried to make it at least a small match but I couldn't handle any more... so I'm very sorry to for all of you."
Alcaraz, meanwhile, expressed sympathy with Sinner, who gave no indication of the exact nature of his illness.
"I'm pretty sure that from these situations you're going to come back better, even stronger than you always do - that's what true champions do," Alcaraz said.
Monday's showdown was the fourth time Alcaraz and Sinner have met in a final this season.