The officer wasn't hurt in the shooting in the South Auckland suburb of Manurewa just before 4am on Wednesday.
Police are looking for Patrick Dixon, a 30-year-old Maori, in connection with the incident.
They have described Dixon as of medium build, 1.77m tall and with a tribal tattoo on his left arm and a tattoo on the left side of his neck.
He has warrants to arrest for unlawful carriage and possession of a firearm, and should not be approached.
Dixon is believed to have connections in Counties Manukau and the Whangamata and Waihi areas, police said.
Anyone with information should contact Counties Manukau police on (09) 261 1300, or call 111. Information can also be provided anonymously through CrimeStoppers on 0800 555 111.
