The incident unfolded on Saturday night when a 28-year-old man was allegedly involved in an armed robbery and another attempted robbery at Mount Sheridan, a southern Cairns suburb.
The knife-wielding man was shot after officers attempted to engage with him near a roundabout, police said.
A female bystander was hit by a stray bullet when police opened fire, triggering an investigation by Queensland's Ethical Standards Command.
Both the man and woman were taken to Cairns Base Hospital for treatment and no police officers were injured.
The 28-year-old was later hit with a string of charges, including attempted robbery and being armed with the intent to cause fear.
He was refused bail to appear in Cairns Magistrates Court on Monday.
Queensland Police Minister Dan Purdie was reluctant to comment in detail on the incident as it was under investigation, but he said he had seen footage of how it unfolded.
The officers involved were highly trained and appropriately equipped, he told reporters on the Gold Coast on Sunday.
"I acknowledge the situations, the dangerous situations, police have put themselves in," Mr Purdie said.
The incident was the second shooting in Queensland involving police within two days.
An officer was shot and a man killed following a domestic dispute at Yengarie, near Maryborough, on the Fraser Coast, on Friday evening.
The 45-year-old man allegedly approached and fired upon a group of 10 officers attending a call-out during the incident.
A first-year constable sustained a gunshot wound to the leg, with the man believed responsible later found dead in a backyard shed.
The incident is also being investigated by ethical standards with oversight by the Crime and Corruption Commission, reporting to the coroner.
The incidents came as the Queensland government on Sunday celebrated the success of Jack's Law, which was made permanent a year ago.
The law gives police the ability to use handheld metal detectors in all public places, allowing officers to detect deadly weapons before they can be used and intervene before lives are changed forever.
The law is named in honour of 17-year-old Jack Beasley, who was fatally stabbed during a night out with friends at Surfers Paradise in 2019.
Mr Purdie said more than 1300 dangerous weapons have been removed from the streets, potentially preventing countless tragedies.
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