Christian Vitta said the proposed monthly minimum would differ depending on the job sector, but that it should be between 3,372 francs and 3,462 francs, equating to under 20 francs an hour, reported news agencies.
The bill comes two years after voters in Ticino – the least wealthy canton in Switzerland – approved the principle of introducing a minimum wage in a cantonal referendum.
However Vitta's bill has not been universally welcomed, mainly because the suggested minimum is seen as too low.
The aim of a minimum wage is to allow people to live without needing social assistance, according to the Green Party, who proposed the original popular initiative that was backed by the public.
The Socialists agree, feeling the amount suggested by the cantonal government is insufficient.
If opposition mounts, it's likely the bill will be put to a referendum.
Switzerland is regularly named one of the most expensive places in the world to live and there is no minimum wage at federal level.
Though salaries are generally high, what might be considered a decent wage elsewhere in Europe does not stretch far in Switzerland.
In 2014 a federal popular initiative aimed to bring in a federal minimum of 22 francs an hour or 4,000 francs a month, considered by union backers as the minimum needed to get by in Switzerland.
But voters rejected it, heeding warnings from the government that it could weaken the economy.
However in recent years several cantons have toyed with the idea of introducing a cantonal minimum, with Neuchâtel set to be the first.
Jura's parliament also recently voted unanimously in favour of a minimum wage, though the proposal will need to go through a second reading and a potential referendum before it can be introduced.
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