Belgian forward Hazard was already set to serve an automatic three-match ban for his red card in Wednesday's semi-final second leg at the Liberty Stadium, where a goalless draw condemned Chelsea to a 2-0 aggregate defeat.
However, the FA insisted Friday that constituted an "insufficient" punishment for the offence.
"The FA has charged Chelsea's Eden Hazard following his side's League Cup semi-final at Swansea on January 23, 2013," an FA statement said.
"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, 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."
Hazard was sent off by referee Chris Foy for kicking Charlie Morgan, the 17-year-old son of Swansea's biggest shareholder, in the closing stages of Wednesday's match at the Liberty Stadium.
The Belgium international lost patience when Morgan refused to hand over the ball after it had gone out for a goal-kick.
Morgan fell to the ground as Hazard attempted to get the ball from him, with the 22-year-old then trying to kick it from under him but appearing to instead make contact with the youngster.
Some leading figures within English football felt Hazard had been harshly treated already.
"Hazard toe-poked the ball under the boy's body," said Harry Redknapp, the QPR manager. "Why is the kid lying on the ball in the first place?
"The boy was tweeting before the game that he's a super time waster. The way he behaved was disgusting."
In the early hours of Friday, Morgan tweeted: "Crazy 24 hours. Spoke to Hazard and I will not be pressing charges. Be in touch."
South Wales Police confirmed Friday they would not be pursuing the incident.
Swansea chairman Huw Jenkins, speaking before the FA charged Hazard, said he wanted the matter to be dropped entirely.
"Speaking on behalf of the club, it's something we'd quickly like to forget."
Chelsea manager Rafael Benitez refused to comment on the incident but a spokesman for the European champions said: "The club, on the evening, recognised the seriousness of the incident. The player recognised that he was wrong to react in that way.
"The appropriate apologies were made, and the club made every effort to make those happen."