In a raft of changes, persecuted individuals may no longer seek refuge at Swiss embassies, and aid is to be cut drastically to refugees once they arrive in Switzerland.
Under the proposals, refugees are to be given "emergency aid": a bed for the night and between eight and 12 francs ($8.4-$12.5/6.7-10 euros) and a day.
This represents half the current allowance.
Further proposals voted on in the parliamentary lower chamber will also make it much more difficult for refugees to bring anyone but their spouses and children to Switzerland.
If the upper chamber gives this proposal the green light, parents of asylum seekers will not be admitted to Switzerland, unless a specific set of criteria is fulfilled.
These include a requirement for refugees to provide adequate housing and sufficient means to support extended family.
In addition, refugees will now have to wait 10 years before they receive their residency permit, doubling the existing five-year wait. At present the number of people seeing asylum in Switzerland is estimated at 40,000.
Left-wing groups expressed concern at the measures, particularly the removal of family refugee status, claiming it would make the process of integration even harder for those arriving on Swiss soil.
Voting on the measures follows a spike in the number of people seeking refuge in Switzerland in the first three months of the year, up 63 percent from a year ago, according to the Federal Migration Office.
For May, the FMO reported 2,331 requests for asylum, four percent down on April.
Eritreans made the biggest number of requests with 437 applications, 86 more than in April, followed by Tunisians (195, down 23 percent) and Nigerians (193, down 21 percent).