In November 1,963 asylum applications were lodged in the country, 66 percent fewer than the same period last year.
The main reason for the drop in numbers is due to the closing of the Balkans route last March, SEM said in a statement.
“The four final months of 2015 were marked by a sizeable number of migrants arriving in Switzerland via that route. Since it was closed, relatively few asylum seekers arrive in that way,” it said.
The closure of the Balkans route has mostly affected migrants from Afghanistan, it said. In November 2,277 fewer Afghans arrived in Switzerland than in November 2015.
Numbers of Iraqi and Syrian asylum seekers were also down.
The largest group of asylum seekers arriving in November were from Eritrea, with 500 applicants lodged, followed by Syria (166), Guinea (139), Afghanistan (109) and Sri Lanka (92).
The figures mean Switzerland will probably receive far fewer asylum seekers this year than predicted.
Since the beginning of the year 25,441 asylum seekers have arrived in the country, 36.2 percent down on last year's total of 34,653.
The SEM therefore expects the final figure at the end of this year to be less than 30,000, the approximate total predicted in July.
Switzerland has also taken part in two refugee programmes this year.
During November 64 Syrian refugees from Lebanon arrived in the country as part of the UN Refugee Agency's relocation programme for particularly vulnerable people living in refugee camps in countries neighbouring Syria.
Since 2015 a total of 935 people have come to Switzerland in this way, with more due to arrive in December.
The country also last month accepted 49 migrants transferred from Greece and Italy under an EU programme aimed at easing the pressure on those countries.