The goal of the campaigners is to block the purchase of the Gripen fighters, which would cost the mountain country 3.13 billion francs ($3.47 billion).
Under Switzerland's system of direct democracy, citizens can have the last word on a huge array of issues if campaigners muster enough signatures from voters in order to force a plebiscite.
Polls have shown that a majority of voters oppose the Gripen deal.
Approved by the government in 2011 and backed by parliament last year, it cannot be blocked as such.
But opponents have been able to contest the law that allows the purchase to be funded by drawing an annual 300 million francs from the army's budget over ten years.
The coalition campaigning against the deal is steered by the left-leaning Socialists and Greens, as well as anti-militarists, but also includes economic liberals opposed to the price tag.
The opponents also argue that the model of Gripen chosen by the authorities only exists on paper, as its maker, Sweden's Saab, is still developing it.
Last month, Saab's Gripen beat the Rafale, made by France's Dassault, and the F/A 18 Super Hornet built by US company McDonnell Douglas in the race to sell 36 planes to Brazil.
The estimated value of the Brazil deal is $5 billion.
The air force of neutral Switzerland currently has 32 Super Hornets in service, purchased in 1996.
There are currently 166 Gripen fighters in service globally, with 100 in Sweden, 26 in South Africa, 14 each in the Czech Republic and Hungary, and 12 in Thailand, according to Saab.