The child, "who had underlying medical conditions, was briefly hospitalized and died late last week," the Minnesota Department of Health said in a statement on Monday.
Laboratory tests "subsequently determined that the child had the H1N1 novel influenza," said the statement.
Officials gave no further information on the age or sex of the child, or how the child may have contracted the virus.
Health authorities "continue to monitor the situation very closely," said Minnesota epidemiologist Ruth Lynfield.
"This flu is very widespread, and we expect to see many more cases across the state," Lynfield said in the statement.
In their latest statistics out Friday, the Centers for Disease Control and Prevention has confirmed 45 A(H1N1) deaths across the United States, as well as 17,855 confirmed cases.
Swine flu has now infected 35,928 people in 76 countries since the disease was first uncovered in late March, data from the World Health Organization showed yesterday.
Around the world 163 people have died, according to the latest WHO tally of confirmed influenza A(H1N1) cases.
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