The decision comes as a result of sanctions imposed by the British government on Russian oligarchs closely linked to Russian President Vladimir Putin.
Abramovich has had his assets frozen in Britain.
Chelsea may continue to play Premier League matches but may not sell tickets to their home matches and may not buy or sell players.
The Russian oligarch has owned Chelsea since 2003.
The Premier League team plays at home against Newcastle on Sunday.
Only year card holders may enter the arena.