Capsicum spray did not subdue an armed woman who was shot by police at a home southwest of Sydney, police say.

Police officers had been called to the home at Picton on Saturday night where a mother and son were reported to be fighting.

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NSW Police Assistant Commissioner Frank Mennilli said one police officer tried to use OC spray after the pair turned on officers.

“Based on the circumstances I have been told the officers were in fear of being seriously injured,” she said.

“In these matters police officers have a split second to make a decision and then others will spend weeks and months to dissect that decision.”

Mr Mennilli said one shot was fired by police and the woman was hit in the abdomen.

The 54-year-old woman has undergone surgery at Liverpool Hospital and is in a serious but stable condition.

Police would not say what weapon the woman had when they arrived at the home.

A neighbour told Network 10 the woman was “always very cheerful”.

“So that’s a huge shock to hear that,” he said.

A critical incident investigation has been set up to look into the police shooting.