Wawrinka, 31, aggravated the injury during the Rogers Cup in Canada, meaning five of the men's top-10 players will not participate in Rio.
Roger Federer, Tomas Berdych, Milos Raonic and Dominic Thiem have also withdrawn.
"I would like to have witnessed my third Olympic Games," Wawrinka said. "This will not be possible now."
Wawrinka suffered a shock second-round defeat at Wimbledon this year, losing to Argentine Juan Martin del Potro, who was ranked 165th in the world.
The injury is another blow for the Switzerland team after 34-year-old Federer, the world number three and 2012 silver medallist, withdrew with a knee injury.
That leaves just two remaining players - Martina Hingis, whose last appearance at the Games was in 1996, and Timea Bacsinszky - from the initial six-member Olympic team.
World number seven Raonic and world number eight Berdych cited the Zika virus for their pullouts.
Switzerland's world number four Stan Wawrinka has withdrawn from the Rio Olympics because of a back injury.