Last year the government budgeted for 23,000 asylum applications for 2013 but that figure is forecast to hit 30,000.
Karl Schwaar told SRF that costs to deal with political refugees are expected to rise to 1.43 billion francs, 100 million francs more than has been budgeted through a three-year plan.
That spending level would be the highest since 1999, marking an increase of half a billion francs in five years.
The federal government will be forced to seek a supplementary credit in the autumn just to deal with extra expenditures for this year, the result of increased asylum applications.
The government did not specifically pinpoint the cause of the increase, occurring despite tightened immigration regulations.
But the UN Refugee Agency, based in Geneva, last week identified one potential source — refugees from the conflict in Syria.
The number of Syrian refugees registered in neighbouring countries and North Africa jumped by 100,000 to 600,000 in the past month, the UNHCR said.
That number is expected to rise to 1.1 million by next June if the war in Syria continues, the agency said.
Meanwhile, the conflict in Mali has caused nearly 150,000 people to flee the country, the UNHCR said on Tuesday.
The UN Security Council has unanimously supported France’s military intervention in the African country to fight Islamist rebels.
France intervened on Friday over concerns that rebels would take over the country’s capital, Bamako, and destabilize the region.