The woman, referred to in reports only as S.Y., went with her boyfriend to the Bruggerhorn swimming area near the Austrian border on Saturday.
“Suddenly she heard a loud whistle. Then she felt a pain in her lower left leg. It was bleeding very heavily,” 52-year-old lifeguard Christian Baumgartner told online news site, Blick.ch.
“We immediately administered emergency treatment,” Baumgartner said.
“She was responsive but totally shocked.”
Strangely, no one heard a bang or the ricochet from the bullet. It is unclear whether she was shot intentionally or by accident.
Swiss police have yet to determine conclusively which direction the bullet came from, with investigations also being conducted over the border in Austria.
For the moment, police are assuming the shooting was an accident, but have not ruled out a direct attack, said spokesman Bertrand Hug.
The type of weapon has not yet been identified. The bullet, which penetrated deep inside the sunbather’s leg, was surgically removed shortly after she was shot.