The 56-year-old music producer was arrested Tuesday after a boy told authorities he'd had sexual contact with him at his Newark, Ohio home, the Licking County sheriff's office said. The boy made the revelation last week.
Finch, while being interviewed at the sheriff's office, admitted he'd had sex with that boy and others ranging in age from 13 to 17, police said.
Finch is the former bass player for the band and a seven-time Grammy Award winner.
A message posted on his Web site said the allegations against him were baseless.
"We will let due process happen through the legal system," the post said. "And through that, we are sure Mr. Finch will be vindicated from these unfounded allegations."
No date had been set for Finch's arraignment, said Sgt. Kevin Biller, who wouldn't disclose the evidence that led to Finch's arrest or the possible charges against him.
Finch started KC and the Sunshine Band in the 1970s with Harry "KC" Casey, who was a record company stockroom clerk when they met. Their collaboration produced a slew of disco and funk hits including "Get Down Tonight," "That's the Way (I Like It)" and "I'm Your Boogie Man."
He was being held at the sheriff's office on $250,000 bond.