Swathes of Germany and France were badly hit by the cuts late Saturday. Austria, Belgium, Italy and Spain were also affected.
A spokesman for German power company RWE AG said a shortfall in supplies to the European power grid caused many substations to shutdown automatically.
It was not immediately clear what caused the shortage.
Areas of western Germany were without power for a half-hour, delaying scores of trains for up to two hours, Deutsche Bahn spokesman Achim Stauss said.
Officials said thousands of worried citizens overwhelmed emergency services with telephone calls.
In France, about 5 million people were left without electricity, including many in the capital, Paris. In all, about 15 French regions were affected, firefighters said.
France Info radio quoted French power utility Electricite de France as saying that about 5 million people were still without power early Sunday, and that it was not sure when it would be able to bring consumers back online.
Firefighters in Paris said they had responded to nearly 40 calls from people stuck in elevators.