"We've surrounded the fire on three sides, but the wind shifted and sent the flames towards an area that we can't reach by land, where we can only work by helicopter," said the head of the firefighters, Miroslav Kanas.
There have been no injuries reported so far, but initial estimates of losses ran to about 300,000 euros (363,000 dollars).
Slovakian Agriculture Minister Zsolt Simon said on Saturday during a visit to the area that the High Tatras forests would be closed to the public after a dozen fires this year.
In November 2004, a violent storm struck the mountain range, flattening thousands of trees and causing losses of more than 200 million eurosmillion dollars).