The terrorists forced their way into the house in Dooru, about eight kilometres from Srinagar, and took away four rifles, police said.
Mr Andrabi, who is also a close relative of Jammu and Kashmir Chief Minister Mehbooba Mufti, was not present inside when the incident took place.
The injured policeman was taken to a hospital in Srinagar for treatment, police said.
The strike was the second terrorist attack in south Kashmir in 12 hours. Two Hizbul Mujahideen terrorists were killed on Sunday trying to ambush a police party that included three senior officers in Jammu and Kashmir's Pulwama district.
On Saturday night, terrorists barged into a house of a sub-inspector and took his son and nephew hostage and ransacked the house.
The terrorists drove away in the car with the two boys but released them later and set the car on fire, police said.
Jammu and Kashmir has been put on high alert following these attacks that are taking place days ahead of the upcoming parliamentary by-elections in South Kashmir. Polls in Srinagar and Anantnag will be held on April 9 and April 12 respectively.
Prime Minister Narendra Modi is also expected to visit Jammu and Kashmir on April 2 for the inauguration of the Chenani-Nashri tunnel, where he will then address a public rally.