The incident overshadowed the goalless draw in the second leg of the Capital One Cup semi-final at the Liberty Stadium, which saw Swansea progress to the first major final in their history thanks to a 2-0 aggregate win.
It happened just over 10 minutes from time when Hazard lost patience as the ball boy, who Press Association Sport understands to be Charlie Morgan - the son of Swansea director Martin - refused to hand over the ball after it had gone out of play for a goal-kick.
The ball boy fell to the ground as Hazard attempted to get the ball from him, with the Blues player then trying to kick it from under him but appearing to instead make contact with the prostrate youngster.
Several Chelsea players went to tend to the ball boy, who was left holding his ribs, before referee Chris Foy produced a red card.
The ball boy was then led away down the tunnel, but is unhurt.
Hazard will not face police action over the incident after 17-year-old Morgan and his father elected not to press charges, but the Belgian will face an anxious wait to see what punishment the FA may choose to add on top of his automatic three-match ban.
The £32million signing issued an apology through Chelsea TV after the match, claiming he felt he had kicked the ball rather than the ball boy, and spoke to Morgan after the teenager was invited to the Chelsea dressing room.
He said: "The boy put his whole body onto the ball and I was just trying to kick the ball and I think I kicked the ball and not the boy. I apologise.
"The ball boy came in the changing room and we had a quick chat and I apologised and the boy apologised as well, and it is over. Sorry."