Dwayne Lindsey, 33, was taken into custody from a residence in Sunshine North on Thursday afternoon.

He will face an out-of-sessions hearing on Thursday evening.

Emergency services had been called to an apartment block on Isla Avenue, Glenroy  about 8.40am on Sunday because of an unresponsive child.

The baby, reportedly called Chase, was taken to hospital with visible injuries to his body, where he later died.

A man who said he was the baby's stepfather, Chris Hamilton, told Channel 7 that the boy had a playful personalty.

"I always played with his teddy bears and he would smile and laugh every time I used to come in the room."

A woman who said she was the child's aunt, Julie Barnes, said he was a beautiful baby.

"The day he was born, he just melted my heart straightaway. A beautiful little kid."

Mr Lindsey and the child's mother are believed to have moved into the unit in the days before the death.

With Marika Dobbin