Following Woods' arrest early Memorial Day, in which the golfer was seen swaying and unsteady in a police dash cam video of the arrest, Nicklaus, who lives in North Palm Beach, not far from Woods' Jupiter Island home, said: "I feel bad for Tiger. Why don't you try to do the opposite and help him now in the way he inspired us?"
Woods was confused but cooperative when he was taken into custody, on suspicion of DUI, according to a probable cause affidavit.
Woods is scheduled to be arraigned July 5 in Palm Beach County Court.
Kaymer, a two-time major champion, has spoken glowingly of Woods for years, including when he passed the American to become the No. 2 ranked player in the world in 2011.
He is then read his rights while seated with his hands cuffed behind his back. "We're going to take them off in a minute but you have to keep them on for right now".
Tiger Woods attributed an "unexpected reaction" to prescription medicine for his arrest on a DUI charge that landed him in a Florida jail Monday for almost four hours.
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The breathalyzer tests took place more than 1.5 hours after Woods' initial arrest.
Slurring his words as he tried to answer questions from police, Tiger could barely stand up and kept weaving and bobbing, failing to walk a straight line barefoot after removing his sneakers.
On Wednesday, officials released dashcam video from the arrest.
The golf star, 41, was arrested in Florida on Monday after officers spotted a Mercedes parked at the side of a six-lane road, partially in a bicycle lane.
"Obviously a lot of people know what happened to Tiger Woods the last few days", Kaymer said.
Tiger Woods stands between two police officers in Jupiter. In a statement, the 14-time Major victor blamed the arrest on an "unexpected reaction" to prescription medication, and said alcohol wasn't involved. The engine was still running and the vehicle had sustained damage on both bumpers, according to police.