How large is the immigrant population in Minnesota?
In 2010, Minnesota's foreign-born population was about 7.5% of the total population per Selected Characteristics of the Native and Foreign-Born Populations, 2006-2010 American Community Survey 5-Year Estimates, U.S. Census Bureau.
"Immigrants" is a broader term and less easily computed.
The State Demographic Center presented "Immigration Trends in Minnesota".
The MN State Demographic Center explains the issues involved in determining the immigrant population in "Working with Immigrant Data".