The vehicle was parked in the Main Street area of the Co Antrim town when it was targeted at around 3.20am on Monday.
A three-month-old dog which was inside it died.
A woman who tried to put the fire out had to be taken to hospital. She is receiving treatment for injuries which are not thought to be life threatening.
The NI Fire and Rescue Service said the van was "well alight" when crews arrived.
A spokesperson added: "Fire crews attended a fire involving a van.
"It was well alight on arrival of crews. Unfortunately a dog who was in the van at the time died as result of the fire. The fire is thought to have been started deliberately."
SDLP Councillor Pat Catney has slammed those who carried out the attack.
Mr Catney said: "I want to condemn those responsible for an arson attack on a van which has resulted in a woman being taken to hospital and which killed a puppy inside the van.
"This van had been parked on Main Street and I find it shocking that people would burn a van in a public place, displaying such a reckless disregard for human life."
Police said they are investigating the motive behind the arson attack and have asked anyone with further information to come forward.