The animals were attacked at Twelve Oaks Farm in Swanmore at about 23:30 GMT on Friday.
A reindeer called Comet was killed in the attack, a second, called Candy suffered severe injuries.
Hampshire Constabulary said officers had seized five dogs found loose on the land in connection with the attack, but no arrests have yet been made.
Hundreds of messages have been posted on the farm's Facebook page.
One person said: "The loss of any animal is very upsetting but to lose them this way is horrific."
A reindeer has been killed and another seriously injured by a pack of dogs at a Hampshire petting farm.