With the Games less than 100 days away, Leishman announced his decision in a statement issued via the Australian PGA.
He said he had withdrawn from the event because of fears over the strength of his wife Audrey's immune system.
"Last April, my children and I almost lost my wife to toxic shock syndrome," the statement said.
"Since then, Audrey has been prone to infection and is far removed from 100 percent recovery of her immune system.
"We have consulted with Audrey's physician and, due to her ongoing recovery and potential risks associated with the transmission of the Zika virus, it was a difficult yet easy decision not to participate.
"I missed playing in the 2015 Masters tournament to be at her side when she was originally stricken, and I cannot risk placing her health in jeopardy."
Zika, a mosquito-borne virus that is linked with thousands of babies being born with underdeveloped brains, was declared a global public health emergency by the World Health Organization three months ago.
The virus has been linked to microcephaly in babies.
Leishman, who lost out in a playoff for the Open at St Andrews last year and is golf's world No. 35, took his decision after "a great deal of thought," Australian PGA chief executive officer Brian Thorburn said.
"To be in a position where you have to withdraw from the Masters and the Olympics, the two most significant tournaments a professional can be invited to, all within the space of 12 months, is not a decision made in haste," Thorburn added.
Australian team chef de mission Kitty Chiller said the organization understood "that family must always come first" and respected Leishman's decision not to take part in the Olympics.
