MILWAUKEE—Wisconsin Gov. Scott Walker declared a state of emergency in Milwaukee on Sunday and activated the state’s National Guard, a day after violence erupted in the city spurred by the fatal police shooting of an armed man following a traffic stop.

At a Sunday news conference, Milwaukee Police Chief Edward Flynn identified the man who was shot by police as 23-year-old Sylville K. Smith, who, according to court records, was African-American. The 24-year-old officer who shot Mr. Smith is also African-American, according...