Luping Zeng, 56, was shot in the chest on Monday night in the garage of his MacGregor home while he was packing his car.

A 17-year-old Slacks Creek boy was arrested on Thursday afternoon in South Brisbane.

A 19-year-old man was arrested in the same suburb at 11am on Friday and a 20-year-old was arrested in neighbouring Woodridge minutes later.

The three are now each charged with murder along with robbery and firearms offences.

Detective Superintendent Tony Fleming says the youngest boy didn't know Dr Zeng and robbery appeared to be the motive.

"It was likely this is a crime of opportunity that has escalated and resulted in the death of Dr Zeng," he told reporters on Friday.

The three alleged killers are known to each other, Detective Superintendent Fleming said.

Dr Zeng's wife and two adult children were at home when the shooting occurred.

He was taken in a critical condition to Princess Alexandra Hospital where he died.

Dr Zeng had three decades of medical experience, spoke three languages and was a highly regarded member of Brisbane's Chinese community.

He moved to Australia in 2000 and worked at the Waterford 7-Day Medical Centre and Skin Cancer Clinic.

His patients reacted to the news of his death with disbelief, remembering his gentle and compassionate nature.

The arrests came after police on Thursday released photos of a stolen silver 2013 Hyundai Elantra hatchback linked to the killing.

Police renewed their appeal to the public for help locating the car, which they believe could hold vital clues.

The 17-year-old was remanded in custody while the two older males were ordered to appear at Brisbane Magistrates Court on Saturday.

Australian Associated Press