Mr Allenby, 43, says he may have been drugged before he was taken from the bar on Friday. He was helped back to his hotel by a retired military man.
"I didn't think I was going to survive this one," he told the AAP news agency.
The golfer had been planning to fly out of Hawaii after missing the cut at the US PGA Tour's Sony Open.
Local television said the incident was being investigated as second-degree robbery.
"I was separated from my friend in the bar after we had paid the tab at 22:48 (08:48 GMT) and he went to the bathroom and next thing you know I'm being dumped in a park miles away," he said.
He said a homeless woman spotted him being dumped from a car, after being robbed of his phone and wallet.
The military veteran paid for a taxi for him back to the hotel, he said.
Pictures shown on the Golf Channel showed Mr Allenby with cuts on his nose and forehead and bruising around his eye.
His caddie Mick Middlemo told the channel Mr Allenby woke up groggy with no initial recollection of what happened to him.
Allenby is ranked 271 in the world and has won four titles on the elite PGA [Professional Golfers' Association] Tour.
Australian golfer Robert Allenby says he was kidnapped from a bar in Hawaii, robbed and beaten, before being dumped in a park.