Officers were at a Collinsvale property, near Hobart, on Sunday evening as part of an ongoing criminal investigation when the 37-year-old allegedly shot a single bullet towards police.
"Upon entering the property and driving through the front gate, police became aware that something had struck their vehicle," Assistant Commissioner Adrian Bodnar said.
A single bullet was found near the wheel guard of the unmarked police car.
The woman was arrested before being charged with attempted murder and several firearms offences.
A 38-year-old man at the home was also arrested and charged with firearms offences and attempted aggravated assault.
Both will appear before the Hobart Magistrates Court later on Monday.
Investigators believe the residents didn't realise it was police entering their property when the firearm was allegedly fired.
"Regardless, it is reprehensible that our officers were placed at such risk while performing their duties," Mr Bodnar said.
"This incident could have had tragic consequences, and it was extremely fortunate that no one was physically harmed."
Tasmania Police Constable Keith Anthony Smith was killed in June as he approached a rural property to deliver a court-ordered home repossession warrant.
A 46-year-old North Motton man surrendered at the scene and has been charged with the murder, attempted murder and aggravated assault of the 57-year-old officer.
Victoria Police officers Neal Thompson and Vadim de Waart-Hottart were shot dead while attempting to serve a warrant to Dezi Freeman in Porepunkah, about 300km northeast of Melbourne, in August.
Freeman has been on the run for more than two months despite a large-scale police effort scouring dense bushland and offering a $1 million reward for information that leads to his capture.
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