Police are appealing for help to identify the man after the boy underwent surgery following the "terrifying" incident on Tuesday.
The baby was with family at Hanlon Park, Stones Corner at midday when a man approached, police said.
He then poured a hot liquid believed to be coffee on the child in what police described as a deliberate and unprovoked act.
"It is callous and cowardly," Detective Inspector Paul Dalton told reporters on Wednesday.
"Going to a park on a beautiful winter's day in Brisbane, enjoying your time ... to be attacked like this and approached like this, it must be terrifying."
The boy underwent surgery after being rushed to the Queensland Children's Hospital with "non-life-threatening" but serious burns and remains in a stable condition.Â
"Both her (the mother) and the baby's father are obviously very distressed," Det Insp Dalton said.
"In 35 years of being a police officer I've never come across a job where a child this young in these circumstances has been attacked.
"I can't think of it. I'm not aware of it happening."
Police on Wednesday released CCTV footage of a man running from the park.
The man was wearing a black hat, glasses, a shirt and shorts and is believed to be aged around 30 to 40 with a proportionate build and tanned skin.
Anyone with information is urged to contact police.
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