The company said it had not been paid for previous deliveries.
The Finnish grid operator said Russia provided only a small percentage of the country’s electricity and that it could be replaced from alternative sources.
On Thursday, Russia threatened to take “retaliatory steps” after Finland said it planned to join Nato.
Finland shares a 1,300-km (810-mile) border with Russia, and has previously stayed out of Nato to avoid antagonising its eastern neighbour. However, since Russia’s invasion of Ukraine there has been a surge in public support for Nato membership.
On Sunday Finland is expected to formally announce its plan to join.
The decision by Rao Nordic has not been explicitly tied to Finland’s decision.
The Russian state-owned firm said: “This situation is exceptional and happened for the first time in over twenty years of our trading history”.
Neither Rao Nordic nor the grid operator in Finland, Fingrid, explained what was behind the payment difficulties.
Last month Russia cut supplies of gas to Bulgaria and Poland after they refused to comply with a demand to pay in roubles, a change they said would contravene western sanctions.
This week Russia’s Gazprom announced it would stop supplying gas via the Polish part of the Yamal-Europe pipeline.
Fingrid said it did not expect electricity shortages as a result of the shut off, as only around 10% of Finland’s electricity is supplied from Russia.
“The lack of electricity import from Russia will be compensated by importing more electricity from Sweden and by generating more electricity in Finland,” said Reima Päivinen, senior vice president of power system operations at Fingrid.
Demand is also decreasing as the weather gets warmer, while a significant amount of extra wind power generation is expected to come on stream. A new nuclear power station, expected to open this summer, would more than make up for the lost supplies from Russia, Fingrid added.