Several bullets were discharged into the front bedroom window of a house at Chigwell.
Tasmania Police are investigating the incident, which they are treating as a targeted attack.
Detective Inspector Craig Joel said the incident occurred just before midnight on Sunday evening at a property at Tootonga Street.
The sole occupant of the house, a 44-year-old woman, was uninjured during the incident but damage was sustained to the house.
“Tasmania Police are treating the shooting as a targeted attack and are following particular lines of enquiry including the possibility there was a dispute between the woman and a group of people in Glenorchy earlier in the day,” Detective Inspector Joel said.
Police are also seeking any information about a small, dark-coloured car, which was seen in the street.
Any information about the shooting, including about the car, can be provided to Glenorchy CIB on 131 444.
Alternatively, information can be provided anonymously by calling Crime Stoppers on 1800 333 000 or online at crimestopperstas.com.au