The eight are suspected of laundering money for the Taganskaya criminal group, police said in a statement.
They are accused of tax fraud, document falsification, influence peddling and membership in a criminal organisation.
"This is one of the largest criminal organisations in Moscow, which specializes in extortion from businesses that it pushes into bankruptcy and takes control of," the statement said.
"The searches carried out as part of the operation allowed investigators to confirm that Taganskaya used our country to launder money from its criminal activities in Russia," it added.
The Guardia Civil is investigating other evidence that points to the perpetrators’ involvement in other serious crime areas including coercion and corruption, Europol said in a statement.
More arrests many follow, the European law enforcement agency said.
Spain's Mediterranean coast has become a top destination for Russian tourists, especially the Balearic Islands and the beach resorts near Barcelona in the northeast.
The influx of big-spending Russian tourists has been welcomed by hotel operators even as it raises fears that the region could become a magnet for criminal organisations.
In January police arrested five people in Lloret de Mar near Barcelona who are suspected of laundering large sums of money for Russian criminal gangs linked to Semion Mogilevich, one of the FBI's 10 most wanted fugitives.
Police said searches carried out as part of that investigation found evidence that the suspects had links with major Russian crime groups like Solntsevskaya and Solomonskaya.
In July, police raided the Majorcan chapter of the Hells Angels Motorbike Club in what was described as a major blow to the island's powerful German mafia.
Some 200 police and Civil Guard officers made 25 arrests in 31 raids in an operation directed by Spain's National High Court.
Most of the club's members arrived on the island from Germany after authorities in that country cracked down on the group in 2009.
The group raised money mainly by forcing women into prostitution across Germany and extorting cash from people they threatened to harm if they were not paid.