Spain's government outraged the local government, residents and environmental groups in August by giving oil group Repsol the all-clear to explore near the islands' coasts.
Conservative regional president Paulino Rivero told reporters on Thursday he would let residents over 16 vote on November 23rd on the plan, which he fiercely opposes.
"Do you think the Canaries should change its environmental and tourism model for the sake of oil and gas exploration? That is the question that will be put to the vote," he said.
Residents of the archipelago off the northwest coast of Africa fear Repsol's explorations will harm the environment and disrupt the tourism industry on which their economy relies.
The company has been authorized to spend three years probing below the sea bed about 50 kilometres (30 miles) from the islands of Lanzarote and Fuerteventura.
Under the terms of the licence, Repsol must provide a deposit of €20 million ($25 million) "to cover its environmental responsibilities".
It must stop its explorations if an earthquake stronger than magnitude 4.5 strikes the region.
Those safeguards have not convinced Rivero and local protesters, however.
A local civil campaign group has called for demonstrations across the seven islands of the archipelago on October 18th under the slogan "We live here, we decide here".