Britain said the oligarchs had their assets frozen because of their connections to Russian President Vladimir Putin
Officials said the seven have a collective net worth of nearly $20 billion.
Despite the sanctions, the British government said that Chelsea can continue playing matches in the English Premier League.
Abramovich had put the club up for sale, but Britain's asset freeze and sanctions on him bar that process under the terms of the license granted to the club.
Britain's minister for sport, Nadine Dorries, said the government had issued a special license to enable Chelsea to play fixtures, pay staff and enable ticket holders to attend matches.
She said the government did not want to harm the reigning European and world soccer champions.
The government said the license would be kept under review.
Abramovich is also the largest shareholder of Russian steelmaker Evraz.
Its London-listed shares were down more than 12% in early trade.
