Bencic had been expected to be part of the Switzerland squad along with Timea Bacsinszky in Brazil, however she has been struggling with a wrist injury sustained at Wimbledon.
And although she has recovered from the injury, Bencic says she will not be ready for Rio and instead will turn her attentions to the US Open after the Games.
"It is with a heavy heart that I have to withdraw from this year's Olympics," she posted on Twitter.
"Although I have recovered from the wrist injury that I sustained at Wimbledon at the end of June, I am behind in my training schedule and am therefore not completely ready to take part.
"I will be using the next few weeks to fully prepare with my coach Melanie Molitor for Cincinnati, New Haven and the US Open."
On Tuesday, Bencic's compatriot Roger Federer, the men's world number three, pulled out of Rio with a knee injury that has ended his 2016 season.
Federer announced earlier this week he will not feature at the Olympics as he gives his body enough time to fully recover after his recent knee problems – the 17-time Grand Slam winner not set to feature on the ATP Tour again until 2017.
The US Open 2016 begins in New York on 29 August.