Chelsea playmaker Hazard was sent off by referee Chris Foy for kicking Charlie Morgan in the closing stages of the 0-0 draw.
The Belgian lost patience when the 17-year-old ball boy 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.
Hazard was shown a red card for violent conduct, incurring an automatic three-game ban as a result.
However, the FA alleges "the standard punishment that would otherwise apply was clearly insufficient" and has charged Hazard. If the charge is proven then the Belgium international will have his ban extended.
A statement read: "The FA have charged Chelsea’s Eden Hazard following his side’s League Cup semi-final at Swansea City on 23 January 2013.
"It is alleged that Hazard’s behaviour in relation to a Swansea City 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 29 January 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."
Meanwhile, Swansea chairman Huw Jenkins has described the police investigation into the Hazard incident at the Liberty Stadium as "remarkable".
While Morgan insists he has no intention of pressing charges, South Wales Police have been obliged to continue investigating the incident after receiving three complaints.
Jenkins, though, is incredulous and just wants to move forward after his club's achievement of reaching their first major cup final was overshadowed by the incident.
Jenkins told Sky Sports News: "On a personal note I find it remarkable that there is any thought of police action.
"Things are done in the heat of the moment and probably everybody looks back and wishes things had been done differently. We accept how things are and all move forward.
"I want everything to get back to normal as quickly as we can, move on and look forward to our next game against Sunderland."
Jenkins would like to see the investigation dropped and said: "That would be my personal feeling, but I can't control what others are going to do. Speaking on behalf of the club, it's something we'd quickly like to forget."