The attacker, who has an extensive criminal past, did not know the victims, he said.
The Idaho Statesman newspaper said the apartment complex catered to low-income families and was run by a Boise nonprofit.
Kinner was due to appear in court on Monday.
Boise Mayor Dave Bieter said the “horrific attack” did not represent the state capital, which is the largest city in Idaho and has some 225,000 residents.
Idaho is deeply conservative, particularly outside of Ada County where Boise is located. The issue of whether to welcome refugees to the state has proved controversial.
In 2015, opponents of a federally funded refugee welcoming center in Twin Falls, Idaho, campaigned unsuccessfully for the facility to be closed.