Each of Switzerland's 26 cantons can set its own corporate tax rate, but the federal government would impose a top-up tax to ensure companies are paying 15 percent, raising up to 2.5 billion Swiss francs ($2.76 billion) in tax revenue.
That would still leave Switzerland charging around half the level of corporation tax as countries such as Germany and Japan and lagging an average rate of around 21% in European Union states.
Under the proposal, 75% of the extra cash would go back to the cantons and 25% to the central government.
Fabian Molina, a lawmaker with the left-leaning Social Democrats (SP), described the revenue distribution plan which would see wealthy cantons such as Zug and Basel which have low tax rates having the most cash returned as "absurd".
The planned scheme would allow cantons to spend the extra income on subsidies to attract and retain business. Among the measures under discussion are childcare, research grants and extra training.
Finance Minister Karin Keller-Sutter supports the new tax. She said last month, "this minimum tax is coming, with or without Switzerland."
Under the OECD scheme, if companies pay rates below 15% in a particular country, their home governments could "top up" their taxes to that level, eliminating the advantage of shifting profits.
Swiss Holdings, a group representing 62 multinationals in Switzerland including Nestle, Johnson & Johnson, and IKEA, supported the minimum tax.
"A yes would ensure that Switzerland is ready in time. It would send a sign to the international community that we should no longer be considered a tax heaven," the organisation said.
"And maybe most compelling for many: It would ensure that the money will stay in Switzerland."
Business groups have also backed the proposal as it will provide certainty even if Switzerland loses some of its low-tax allure.
"No other country is going to have lower taxes either. We want the additional tax revenue to stay in the country, and be used to improve its attractiveness for businesses," said Christian Frey, from Economiesuisse, a lobby group.
Stefan Kuhn, Head of Tax and Legal at KPMG Switzerland, said the top-up tax "gives cantons the money to do something smart to remain competitive."