The fire has spread some 8 sq km (800 hectares) since it started in a nature reserve on the north-east coast of the island late on Tuesday evening.
Local authorities have cut off access to the forest around the Mount Teide volcano, Spain’s highest peak, and say secondary fires have now broken out.
The main blaze is spreading through woodland and ravines in the Candelaria and Arafo areas, making it difficult for firefighters to tackle.
Photos show large flames engulfing parts of the forest, and thick plumes of smoke billowing into the sky.
Wildfires have raged in many parts of the world this summer, including in southern Europe, northern Africa, Canada, and Hawaii.
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