A woman who allegedly threatened police officers with an axe has died after she was shot by police.

South Australia Police said they were contacted around 2am on Thursday with reports of an armed woman in the Adelaide suburb of Firle.

When they arrived at the property on Gwynne Street, the officers were allegedly threatened by a woman armed with an axe.

A SA Police spokesperson said a Taser was deployed but it was ineffective.

The woman, whose age has not been released, was then shot by police.

She received first-aid from police officers and paramedics but died at the scene.

A police officer suffered minor injuries during the incident.

Major Crime Investigation Branch detectives, Forensic Response Section officers, and Internal Investigation Section representatives are on the scene and an investigation is underway.

A report will be prepared for the coroner.

Gwynne Road remains closed.

More to come...