The cause of Wednesday's blast in the Zaitun district of Gaza City remains unclear.
Palestinian witnesses said an Israeli helicopter had fired a missile at the vehicle, but security officials said they are investigating whether the cause was a bomb detonating prematurely.
A photographer at the scene said he had seen fragments of a missile with Hebrew writing on it while witnesses said Israeli army helicopters had been seen flying overhead at the same time.
The three, who included a father and his young son, were injured as they were walking close to the car in the north of the city.
Initial information indicated that the victims were Hamas members but the sources later said the three were civilians and that the suspected Hamas members were seen running away from the scene of the explosion.
An Israeli military spokesman said he had no immediate information on the event.