A man who was allegedly armed with a knife is fighting for life after being shot by police outside a shopping complex south of Brisbane.

Police were called to Logan Central on Ewing Road just before 6pm (7pm AEDT) yesterday following reports a knife-wielding man was making threats to members of the public.

Video footage shows the man smashing the windows of a car and jumping on its roof before pulling out a knife and allegedly threatening others.

"He's on there, jumping on it, destroying the roof, and next thing you know he pulls out a knife," one witness who did not want to be identified said.

"The guy keeps yelling, 'I'll come for you guys with the knife', so it was pretty scary," another witness said.

When officers attempted to engage with the 27-year-old man, police allege he approached them with a weapon.

Police then opened fire and shot the man.

Officers provided first aid at the scene and he was taken to the Princess Alexandra Hospital in Brisbane for treatment under police guard.

He remains in a life-threatening condition.

It is understood police will speak to the man once he recovers.

Nobody else was injured during the incident, and police say there is no ongoing threat to the public.

A crime scene has been declared and the Ethical Standards Command and Crime and Corruption Commission will investigate the shooting.

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