"It is extremely lucky no one inside the house was passing through the area at that time or we could have been dealing with an injury or worse."
Police said their investigation has not determined who was responsible, but they are satisfied it was not intentional.
Anyone who has information can call 105 and quote file number 210407/7674.
Police said they remind hunters to always point guns in a safe direction and identify the target and what is beyond it.
A neighbour of the Puketitiri family, who did not want to be named, said poaching had been an issue in the area in the past, including the week before the stray shot incident.
"They are prolific up here at the moment," they said.
"It's quite unnerving."
Hawke's Bay Police also issued a reminder about the Seven Basic Firearms Safety Rules:
1. Treat every firearm as loaded
2. Always point firearms in a safe direction
3. Load a firearm only when ready to fire
4. Identify your target beyond all doubt
5. Check your firing zone
6. Store firearms and ammunition safely
7. Avoid alcohol and drugs when handling firearms