The Panama-registered Fremantle Highway was transporting 2857 cars from Germany to Egypt, 25 of them electric.
An electric car was the suspected source of the blaze, a coastguard spokesperson said, adding that the ship was still burning.
The 199-metre ship, which had departed from the German port of Bermenhaven, was successfully towed out of shipping lanes early on Wednesday, Dutch broadcaster NOS reported.
The ship was sailing 27km north of the Dutch island of Ameland, with 23 crew onboard, when the fire started on Tuesday night, a statement said.
The crew had tried, but failed, to extinguish the fire, the coastguard statement said.
The injured crew were taken by helicopter to medical facilities on the mainland. They suffered smoke inhalation, or were hurt during the evacuation, a spokesperson said.
A spokesperson for Shoei Kisen Kaisha, a Japanese ship leasing company that manages the Fremantle Highway, was not immediately available for comment.
It is the latest fire to affect a car carrier.
Earlier this month, two New Jersey firefighters were killed and five injured while battling an intense blaze on a cargo ship carrying hundreds of vehicles.
A fire destroyed thousands of luxury cars on a ship off the coast of Portugal's Azores islands in February last year.
