Officers were called to an address in Benjamina Street at Mount Sheridan, a southern suburb of Cairns, following reports of a man armed with knives, shortly after 5pm on Saturday.
Queensland Police said in a statement the officers attempted to engage with the man before he was shot by them.
During the altercation, a civilian woman also sustained a gunshot wound.
Both people were treated at the scene before they were taken to Cairns Hospital.
Police said there was currently no threat to the public.
Far Northern Region Assistant Commissioner Graeme Paine is expected to address media in Cairns on Sunday morning.
The incident follows the shooting of a police officer and the death of a man following a domestic dispute at Yengarie, near Maryborough, on the state's Fraser Coast, on Friday evening.
It is alleged the 45-year-old approached and fired upon a group of 10 officers attending the call-out.
A first-year constable sustained a gunshot wound to the leg, with the man believed responsible later found dead in a backyard shed.
The Queensland government this week announced it was boosting police resources and frontline safety through equipment upgrades, mental health support and recruitment milestones.
The $14 million investment will deliver more than 14,000 new Austrian-made Glock 45 service pistols from the end of the year.
The weapons will replace ageing handguns from 1998, "ensuring every officer has modern, reliable equipment to help them respond to dangerous situations and continue making Queensland safer".
7°C