Royal Parks Police shared footage showing a spaniel chasing a fallow deer near Sheen Cross and forcing it away from its herd.
Due to severe injuries, the deer was later euthanised.
Search for dog owner
Witnesses reported the dog's owner walking away from the scene with the animal on a lead.
The man, described as wearing a red beanie, black coat, and blue jeans, has not yet been identified.
Paul Richards, manager of Richmond Park, called the event "deeply distressing" and stressed the significance of responsible dog ownership. He reminded park visitors that it is illegal to let dogs chase wildlife, highlighting the need for pets to be under strict control.
Keep dogs on lead
If a dog’s recall ability is unreliable, owners are advised to keep them on a lead or choose alternative walking locations.
Richards also noted specific regulations requiring dogs to be leashed during deer birthing season and in designated nesting areas.
On average, three to four deer are killed annually by dogs in the park.
The Metropolitan Police have urged anyone with information to come forward as enquiries continue.