The 32-year-old male suspect, who was not identified in the police statement, was charged with three felony counts of identity theft and attempted theft, and a felony charge of unauthorized possession of confidential personal information.
Police said they identified numerous charges to Allenby's credit cards at stores around Oahu, and added that the suspect was arrested at the Oahu Community Correctional Center where he was being held on a contempt warrant for a separate incident.
Allenby, 43, has said that he went out for drinks after failing to qualify for the Sony Open in Honolulu last month. He said he was separated from his caddy and a friend after they had paid their tab.
He told Reuters then that the next thing he recalled was waking up groggy in a park miles away from the bar to find he had been beaten and robbed of his wallet, cell phone, cash and credit cards.
Allenby, who was left with facial injuries, said a homeless woman he encountered in the park told him she had seen a few men drive up in a car and throw him out of the vehicle.
Police have previously said detectives were probing the case as a robbery and credit-card fraud investigation. Police made no mention in their statement on Wednesday of Allenby's kidnapping account.
Honolulu police could not be immediately reached to provide additional details.
Allenby, who has won four times on the U.S. Tour, most recently at the 2001 Pennsylvania Classic, pulled out of a PGA Tour event in California last month to recover from the ordeal, he said.
The golfer turned professional in 1992 and has won 18 tournaments around the world including 13 on the PGA Tour of Australasia.