The attack is the latest in a series of sporadic attempts by militant groups that continue to target police officers, decades after a peace deal largely ended sectarian violence in the region.
Northern Ireland police say the car was hijacked in the Twinbrook area of west Belfast late on Saturday and a gas cylinder device was placed in the trunk.
The man was ordered to drive the vehicle to Dunmurry police station, Deputy Chief Constable Bobby Singleton told a news conference on Sunday.
The vehicle was abandoned outside the front of the station, prompting police to activate an alarm and evacuate nearby homes.
"A number of residents, including two babies, were being taken to safety by officers when the device exploded, engulfing the vehicle in flames and sending debris in all directions," Singleton said.
No-one was injured in the blast, which police described as "nothing short of miraculous" given the circumstances.
Singleton described the attack as "senseless and reckless" and said the delivery driver had been left extremely traumatised.
Britain's minister for the region Hilary Benn condemned the attack, calling it "shameless and cowardly."
Police said an evacuation operation was still underway in the area and some residents remained unable to return to their homes.
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