Between 3.30pm and 4pm, teenagers were seen setting fire to the silver Volkswagen Golf in Tithe Barn Road.
They were then seen running off in the direction of the Morrisons car park.
Raymond Hepp, who witnessed the fire and shared a video of the arson, said he did not see what caused the fire but he heard it.
Raymond said: "I was in my room resting, watching a movie, when I heard a really loud noise.
"First I was thinking that the neighbour above me had dropped something really big on the floor, like some kind of furniture, but my mother was calling me to come fast to her room.
"I straight away knew something had happened."
Raymond said he went to his mother's room and said: "I looked outside the window and this car was on fire, big time."
A Northamptonshire Police spokesman said there had been no descriptions or arrests of the offenders.