“My heart goes out to George Floyd, his loved ones and all of us who are hurting right now,” Woods said in a statement on Twitter.
But he said violent protests were not the answer as unrest flared across the United States on Monday.
Tiger Woods said he had the “utmost respect” for police.
He likened the situation to the Los Angeles riots of 1992, after four police were acquitted over the beating of motorist Rodney King.
America is witnessing its most widespread protests since the 1960s after Floyd, an unarmed black man, died while being arrested in Minneapolis.
“I have always had the utmost respect for our law enforcement. They train so diligently to understand how, when and where to use force.
Woods’ statement follows strong comments from a number of athletes including NBA legend Michael Jordan.
Jordan said he was “plain angry”, and tennis player Coco Gauff asked: “Am I next?”
“I remember the LA riots and learned that education is the best path forward,” wrote Woods, the 15-time major-winner.
“We can make our points without burning the very neighbourhoods that we live in.
“I hope that through constructive, honest conversations we can build a safer, unified society.”
AFRICA TODAY NEWS, NEW YORK