Rescue services including a medical helicopter were scrambled to the scene of the accident on a road in the eastern part of the island, a police spokesman said.
The cause of the accident and the status of others aboard was unclear, he said, although faulty brakes have not been ruled out.
The tourists were members of a group staying at the Parador Nacional de la Cruz de Tejeda, local daily Cananrias7 reported.
They were planning to go hiking, the paper reported.
Gran Canaria is a popular holiday destination that forms part of the Canary Islands archipelago lying off the northwest coast of Africa.