Belgian playmaker Hazard was already set to serve an automatic three-match suspension for his red card in Wednesday night's semi-final second leg at the Liberty Stadium.
But the FA deemed that "insufficient" punishment for the offence, prompting an additional charge this afternoon.
An FA statement read: "The FA has charged Chelsea's Eden Hazard following his side's League Cup semi-final at Swansea on January 23, 2013.
"It is alleged that Hazard's behaviour in relation to a Swansea ball boy, for which the player was dismissed in the 78th minute, constituted violent conduct whereby the standard punishment that would otherwise apply was clearly insufficient.
"The player has until 6pm on Tuesday, January 29, 2013 to respond to the charge.
"The FA will remind all clubs of their responsibilities in ensuring ball boys and other personnel around the pitch act in an appropriate manner at all times and will liaise with competitions accordingly."