Anders Ygeman said charter aircraft would be used to deport the migrants but it would take several years.
Some 163,000 migrants applied for asylum in Sweden in 2015, the highest per capita number in Europe.
The numbers have fallen significantly since Sweden imposed tighter border controls this year.
Along with Germany, the Scandinavian country is a prime destination for refugees and other migrants entering the EU illegally.
Of the approximately 58,800 asylum cases processed in Sweden...
EU migrant crisis: Sweden may reject 80,000 asylum claims
Some 163,000 migrants applied for asylum in Sweden in 2015, the highest per capita number in Europe.
The numbers have fallen significantly since Sweden imposed tighter border controls this year.
Along with Germany, the Scandinavian country is a prime destination for refugees and other migrants entering the EU illegally.
Of the approximately 58,800 asylum cases processed in Sweden...
EU migrant crisis: Sweden may reject 80,000 asylum claims