The dog was off-lead and walking about 100m ahead of its owner when it came across the pup and attacked it.
It is understood the owner immediately ran to retrieve the dog and intervene, but was unable to prevent the dog inflicting fatal injuries.
She said it was an important lesson for not only the owner, but also the wider public.
"If you think you can't control your dog, you need to keep it on a lead and this is really important in many places around Hawke's Bay where there are wildlife; Ahuriri Estuary and the beaches where at this time of year, you have got seal pups and the like hanging around."
Seals are protected under the Wildlife Act 1953 and owners of dogs that attack seals could face some hefty penalties of up to $3000.
It is an offence under the Marine Mammals Protection Act 1978 to disturb, harass, harm, injure or kill a seal.
A dog owner whose dog attacks a seal can face prosecution.
Members of the public can help by ensuring their dog is under control, and on a lead at all times.
Kekeno [seals] were once hunted from the northern to the southern tips of New Zealand for their pelts, bringing them to the verge of extinction.
Since being protected, the seal population has increased and they are spreading further north. Sightings are becoming more common on the East Coast.
