He was caught on camera raising his hands to Arsenal defender Laurent Koscielny's face during Chelsea's Premier League win on Saturday.
The incident was missed by referee Mike Dean.
Arsenal's Gabriel Paulista needs to answer an improper conduct charge by Thursday for his behaviour after getting sent off for kicking Costa – while both clubs have been charged with failing to control their players.
Meanwhile, Sir Alex Ferguson has revealed he made sure he was paid more than any of his players as Manchester United manager.
It was guaranteed under a contract he signed in 2010.
More than two years after his retirement, his new book is released today.
Fergie says the success he brought to United was largely down to how he always got his players to recover from disappointment.
