Schneider-Ammann launched a campaign on Tuesday objecting to the proposal, which will be put to Swiss voters in a referendum on May 18th. Switzerland does not currently have a national minimum wage.
If the plan is approved, Switzerland's lowest hourly salary will exceed that of current record holder Australia by more than ten US dollars. Australian workers are entitled to A$16.37 per hour ($14.67).
The UK's minimum hourly wage is £6.31 ($10.55), while Germany recently agreed a €8.50 ($11.69) minimum from 2017. The current US rate is $7.25.
Speaking at a media conference reported by Reuters, Schneider-Ammann said: "The government is convinced it would be wrong for the state to impose a nationwide wage."
"A minimum wage of 4,000 francs could lead to job cuts and even threaten the existence of smaller companies, notably in retail, catering, agriculture and housekeeping."
"If jobs are being cut, the weakest suffer most," he said.
In an interview with newspaper Tribune de Genève, Philippe Leuba, economics minister for canton Vaud, agreed.
Bringing in a minimum wage would compound the problems created by the recent anti-immigration yes vote, he said.
"Don't forget that one franc in two is earned through exports. Our standard of living depends on our ability to export and if we fail to maintain relations with the EU there will be considerable difficulties for the economy, for salaries, for jobs and for apprenticeships. So let's not multiply our mistakes by saying yes to a minimum wage."
In November, Neuchâtel became the first Swiss canton to propose a minimum wage of 20 francs ($21.75), to come into effect in 2015, after residents voted to accept the principle.