Most of the homes without power were in the areas of Varkaus and Pieksämäki. Many households in central parts of the country were also suffering from outages.
Thousands of homes in the south and south west lost supplies during the night, but most services had been restored by morning.
Slippery roads
During the night, winds were blowing at severe gale force of around 21 metres per second off the south coast, particularly around the Hanko peninsula.
Road conditions Monday morning were hazardous in the southern and middle parts of the country because of snow or sleet and ice-covered roads.
Boats stay in port
With high winds and waves of more than four metres, Linda Line cancelled all of its sailings between Helsinki and Tallinn on Sunday, five departures in each direction.
Tallink cancelled one ship crossing from Helsinki to Mariehamn in the Åland Islands. However Eckerö Line says its vessels were sailing on schedule.
The civilian aviation authority Finavia reported no weather-related disruptions to flights. However Blue 1 cancelled its 6.40am flight from Helsinki to Copenhagen due to an industrial dispute in Denmark.