The motion, proposed by a member of the right-wing Swiss People's Party (SVP), was rejected on Sunday by the Landsgemeinde, reported news agencies.
Around 6,000 people gathered under rainy skies for the Landsgemeinde – the canton's open-air public assembly – to hear the arguments for and against the suggestion of Roland Hämmerli which he said would allow people to “live in security in our canton”.
If accepted, the bill would have outlawed the covering of the face in public, effectively banning the burqa and niqab.
Currently the canton of Ticino is the only Swiss canton to have approved such a ban, which came into effect last year.
The idea has also been proposed at federal level, though in March the Swiss upper house of parliament rejected the bill by hardline Swiss People's Party (SVP) MP Walter Wobmann.
However the issue could still be decided by the Swiss public, if a popular initiative on the subject launched by Wobmann gathers the required number of signatures by September.
The Glarus government had recommended that citizens reject the cantonal motion, saying it would be better to wait and see if it goes to a federal vote.
Glarus is one of only two cantons in Switzerland that still vote using a Landsgemeinde. The canton's highest authority, it is held once a year on the first Sunday in May. The various issues on the table are decided by those in favour raising their hands.