His move comes after four-time golf champion Rory McIlroy pulled out this month for similar reasons, while several other Golf big names have also said they won't travel to South America.
"The reason for my decision is my concerns about the possible transmission of the Zika virus and the potential risks that it might present to my wife's future pregnancies and to future members of our family," Day said in a statement published on his Twitter account.
"I have always placed my family in front of everything else in my life. Medical experts have confirmed that while perhaps slight, a decision to compete in Rio absolutely comes with health risks to me and my family. My wife Ellie and I have been blessed with two wonderful and healthy children and our plans is to have more.
"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."
Zika virus disease is caused by a virus transmitted primarily by Aedes mosquitoes and symptoms include mild fever, skin rash, conjunctivitis, muscle/ joint pain, malaise or headache. Zika virus is a cause of microcephaly and Guillain-Barré syndrome in new born babies.
