Hazard was dismissed in the closing stages of Wednesday's Capital One Cup semi-final second leg at the Liberty Stadium after he tried to kick the ball from underneath the 17-year-old but also appeared to make contact with the youngster.
The Belgium international's red card carries an automatic three-match ban but the FA has deemed the standard punishment "clearly insufficient".
Hazard has until 6pm on 29 January to respond to the charge but the police will not take the matter any further.
"We can confirm there is no longer any police involvement in this matter," said a spokesman.
A statement on the FA's website 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 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."
The police launched a probe after receiving three calls from members of the public living in Sussex, Kent and west Wales.
Swansea chairman Huw Jenkins hit out at the police's involvement, telling Sky Sports News: "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."
Speaking before the FA charged Hazard, Jenkins called for the matter to be dropped entirely.
"That would be my personal feeling, but I can't control what others are going to do," he said.
"Speaking on behalf of the club, it's something we'd quickly like to forget."
Chelsea boss Rafael Benitez refused to be drawn on any aspect of the ball boy saga or its implications.
The Spaniard deployed the same evasion tactics used in a press conference earlier this week, saying: "We have two windows: one for football and one for the other issues."
He said Hazard had trained "normally" since the incident and that any disciplinary action taken against him by the club was an "internal" matter.