The federal government on Friday approved this requirement, to take effect on April 1st, after consulting with the cantons and interested parties.
The change modifies an ordinance on the free movement of people dating back to to May 2002.
Citizens of countries from the EU and EFTA can live in Switzerland for up to three months, during which time they can seek employment.
If they do not find a job within that period but want to continue to search for one they must obtain a short stay residency permit valid for three months a year.
Under the new rules, they will only be eligible for such a permit if they have the necessary financial means to support themselves, the state secretariat for migration said.
However, it did not stipulate how the financial means test would be put into practice.
In other words, it is not clear how much money or assets a person will need to show that he or she has the financial means to live in Switzerland independent of government aid.
A change to the federal law on foreigners aims to exclude social aid from going to UE/EFTA citizens and members of their families who come to Switzerland with the the sole goal of finding a job.
Bern is still negotiating with Brussels on a way to implement a cap on EU immigration, approved by Swiss voters in February 2014, that flies in the face of the freedom of movement accord that Switzerland has signed with the bloc.
The EU has warned that any move to nullify the freedom of movement accord will put at risk other bilateral agreements.
Under the timetable laid out by the immigration cap initiative, Bern has less than two years to work out an implementation deal.