Police said the men were not known to the woman.
They asked for a person they believed lived at the home but the young woman did not know the person's whereabouts.
"One of the men held the woman at gunpoint while the other two ransacked her address. When they didn't find the person they were looking for, the group left in a vehicle that had been left idling outside the address, possibly indicating there may have been a fourth person involved.''
Forensic analysis is being completed on several items seized from he home during a scene examination.
Investigators have also confirmed the gun used by one of the intruders was a double-barreled shotgun.
Ms Hooke said police were attempting to locate a previous occupant of the address. That person, who has not been named, was believed to be outside the Ashburton area.
"Establishing the facts in this incident may take some time. The fact that it occurred at night, in a remote location and well away from neighbouring properties makes it a challenge,'' Ms Hooke said.
Anyone with information should call Ashburton Police on 03 307 8405 or Crimestoppers on 0800 555 111.