The mosquito-borne Zika virus, which the World Health Organization says is spreading rapidly in the Americas, can cause crippling defects in babies and has been linked to the neurological disorder Guillain-Barre in adults.
"The reason for my decision is my concerns about the possible transmission of the Zika virus and the potential risks that it may present to my wife's future pregnancies and to future members of our family," Australian Day, 28, said in a statement.
"While it has always been a major goal to compete in the Olympics on behalf of my country, playing golf cannot take precedent over the safety of our family. I will not place them at risk."
The decision mean Australia's top three golfers have now withdrawn their names from consideration for the Games with world number eight Adam Scott blaming his busy schedule and Marc Leishman, who is ranked 39th in the world, also citing Zika.
"We respect Jason's decision," the Australian Olympic Committee (AOC) said in a statement. "He is a family man and he has put his family first."
Ireland's Shane Lowry, the world number 25 who finished joint runner-up in this month's U.S. Open, also withdrew on Tuesday and said his decision was based on firm medical advice.
"While I am bitterly disappointed to be missing out on that experience and the opportunity to win an Olympic medal for Ireland, on this occasion I have to put my family's welfare first," said Lowry who recently married.
Ireland Olympic golf team captain Paul McGinley said the withdrawals were not good for the image of the sport.
"I agree it doesn't particularly reflect well on golfers when they seem to be the only ones withdrawing but when it is for their own personal reasons, we have to respect that," he told national Irish broadcaster RTE.
"The risk is very, very, very small but ultimately it's a risk they're not willing to take."
The Rio Olympics, the first in South America, take place from Aug.5-21.
(Reporting by Padraic Halpin and Nick Mulvenney, Editing by Ed Osmond/Greg Stutchbury)
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