A man in Minnesota deliberately dropped his five-month-old son headfirst on the floor because the baby was crying and fussy, prosecutors say.

The baby later died of blunt force trauma.

Matthew Hoisser, 35, is charged with second-degree murder in the April death of his son, Gus.

Hoisser's bail was set at $350,000.

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St. Paul Pioneer Press reports a Washington County judge also ordered Hoisser to have no contact with his wife, Nicole, who is pregnant.

Hoisser's lawyer, John Leunig, says the order isn't necessary because Hoisser's wife supports him.

Matthew Hoisser, charged with murdering his son Gus. Photo / Supplied
Matthew Hoisser, charged with murdering his son Gus. Photo / Supplied

A criminal complaint says Hoisser told investigators he was frustrated because the baby was "being difficult" so he dropped him. The child died of blunt force trauma several days later at Children's Hospital in Minneapolis.

According to St. Paul Pioneer Press, baby Gus's obituary said he died on April 30.

"Gus was a sweet, beautiful baby, a source of joy to his parents, and beloved by all who knew him," his obituary stated. "He loved riding on his daddy's shoulder and hearing his mommy sing, especially Rainbow Connection and will always remain their precious 'Snuggamonkey.' "

The Pioneer Press reported that during the baby's autopsy, the medical examiner found a second head injury that had "occurred prior to the most recent injury … likely within a week or two of the infant's hospitalisation."

Hoisser told police he had caused that injury while changing his son's diaper a few weeks prior to his death.