The Dublin Convention, which requires migrants to claim asylum in the first European country they arrive in, should be "re-examined", the minister told journalists in Bern, the ATS news agency reported.
The migrant burden is being borne disproportionately, Sommaruga said, with Italy carrying the heaviest load.
She said that, with between 1,000 and 2,000 asylum seekers arriving in Italy every day, the system — which non-EU member Switzerland is party to — had come under intense pressure.
Sommaruga said asylum seekers could be spread more evenly across Europe, depending upon the wealth and population size of the host countries.
But such a solution was unlikely to receive much backing, she acknowledged, even in wealthy Switzerland, following a string of referendums in recent years hostile to immigration.
The country has faced a recent surge in the number of asylum seekers, with dozens arriving each day to already overflowing asylum centres.
Altering the convention will not be easy, the Social Democrat admitted.
"I have never yet heard a reasonable proposal that could serve as an alternative."
There are currently no plans to revise or replace the convention.
Switzerland's largest party, the populist rightwing Swiss People's Party (SVP), recently said it would push for a popular vote aimed at restricting the right to seek asylum to those who arrive in the country by plane.
The SVP argued that since Switzerland is surrounded by EU countries, anyone arriving by land would necessarily be coming from a "safe" country, ruling out their asylum claim.
Sommaruga rejected that argument as callous, insisting that such a restriction would stop fleeing migrants from coming to Switzerland.
Swiss authorities have said they expect some 24,000 asylum seekers to arrive in the country this year, up 11 percent from 2013.