The storm is the second in two days to sweep over the two countries following a string of extremely hot and dry days.
At least two people were injured in Slovenia as the winds broke trees and blew off roofs.
Public broadcaster RTV Slovenia reported that one person was killed and another was injured when a tree fell on them in the Lake Bled area.
The storm started around 4p.m., suddenly darkening the air as blinding rain created flash floods and winds swept across the city.
It halted the city transport, caused power outages and left streets blocked with fallen trees.
On Tuesday evening, Slovenian authorities said tens of thousands of people were left without electricity and scores of campers evacuated their camps as strong winds overturned their tents.
The greatest damage was inflicted on high-altitude forests, reported the official STA news agency.
Authorities warned climbers in the Alpine country to stay away from those areas.