Turnout was around 42 percent.
A Swiss law introduced in 2010 bans smoking in all public buildings, though small cafes and bars under 80 square metres are exempt.
Isolated smoking rooms are also allowed in restaurants if they are well ventilated and staff are in favour. Some cantons including Geneva have stricter regulations.
The new draft law, promoted by a Swiss anti-smoking group, sought to ban smoking entirely in all public places, but would have allowed people to smoke in a workplace if they were alone there.
The bill's authors say in cantons where similar laws exist, the incidence of strokes has fallen by 20 percent and respiratory illnesses by 20 percent.
The Swiss Federal Government had recommended a vote against the new bill, claiming existing laws against smoking in public were sufficiently harsh.