Damage caused by a storm on Sunday night was created by more lightning than usual, which is unusual in autumn, Elektrilevi said.
In Haapsalu, in western Estonia, the wind was so fierce it ripped a roof off an apartment building that smashed into cars parked below. Trees and gravestones were also battered in the city cemetery.
"As far as we are concerned, the storm started at around 10 p.m. last night and affected mainly north-western Estonia, i.e. Harju County, Lääne County and the islands," said Elektrilevi's Rasmus Armas.
By 5 p.m. on Monday, electricity had been restored to 20,000 households although another 1,000 will have to wait a little longer.
The power outages were mainly caused by trees falling onto powerlines.
Crews are prepared to fix the damage but they are not sent into the forest at night, Armas said.
Many people have been better prepared for power cuts this year and have invested in generators, Mondays "Aktuaalne kaamera" reported.
The emergency services said the challenges it faced were typical for the conditions.
"We still had a few calls, nothing very extraordinary. Just a fairly typical day. There were 104 calls from all over Estonia, if I'm not mistaken," said Ragnar Neudorf, command chief of the rescue agency Keila and Paldiski.
Weather forecast Taimi Paljak said storms are not unheard of at this time of year.
But there has been more lightning than usual.
"There have always been thunderstorms like this, [moving] in a band across Estonia and with very powerful gusts of wind, but this is more common in summer," Paljak explained.
Strong winds and rain are forecast for the coming days.
Editor: Helen Wright