According to the BBC, the blaze began early on Saturday (15 July) and has consumed more than 11,000 acres of land and at least a dozen homes.
Quoting local officials, the news organisation said some 4,255 people had been evacuated but others are declining to leave.
The fire began in the area of El Pinar in the north-west of Puntagorda, before spreading south towards the town of Tijarafe.
It comes amid a 40C-plus heatwave which has brought soaring temperatures to areas in southern Europe such as Spain, Italy and Greece.
Less than two years ago a volcano eruption on La Palma destroyed around 100 houses and forced thousands of locals and hundreds of tourists to evacuate.
