Uneeb Ullah, 28, was charged after his three-month-old son died in a Brisbane hospital in what police described as a "terribly tragic event".
Ullah was home alone with the boy at the time of the alleged injuries and took him to Ipswich Hospital west of Brisbane on October 1, police said on Wednesday.
The child had arrived at hospital with "significant internal injuries", sparking a police investigation.
"Hospital staff contacted police due to the nature of those injuries," Detective Inspector Mick Manago said on Wednesday.
The infant was transferred to a Brisbane hospital and died on Tuesday afternoon, almost a week later.
Ullah was "surprised" when he was later arrested, Det Insp Manago said.
But he would not comment on what Ullah said to police, or would he discuss the boy's injuries.
Support has been thrown behind the devastated mother who was in a relationship with Ullah and had no other children, police said.
"The boy's mother is extremely upset as you can imagine," Det Insp Manago said.
"This is a terribly tragic event involving a very vulnerable, young member of the community.
"She's struggling but we are offering all the support that we can."
The devastating case had been incredibly tragic for all involved, including police and hospital staff, he added.
Police released an image of the young boy on Wednesday afternoon at the request of the family.
"We ask on their behalf that media respect the family's privacy at this time," a spokesperson said.
Ullah was not required to appear when his matter was mentioned in Brisbane Magistrates Court on Wednesday.
Kirstyn Nicholson, a Legal Aid solicitor representing Ullah, did not apply for bail and sought an adjournment.
Ullah was remanded in custody until the matter returns to court on October 26.
Det Insp Manago said he would not speculate on further charges.
"We will conduct a thorough investigation," he said.
"If we identify any further criminal offences, we will certainly commence prosecution."
He said the nature and dynamics of Ullah's relationship with the mother would form a large part of their investigation moving forward.
The child had been on life support before succumbing to his injuries on Tuesday, Det Insp Manago said.
Ipswich Child Protection Investigation Unit detectives, assisted by the Child Trauma unit, arrested Ullah that night, police said.
Ullah did not have a criminal record beyond minor traffic offences and the family did not have prior interactions with police, Det Insp Manago said.
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