The astonishing incident, the latest to blight Chelsea's season, happened with just over 10 minutes remaining of the Capital One Cup tie, which the Blues lost 2-0 on aggregate.
The game was goalless on the night and Hazard lost patience when the ball boy 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 forward then trying to kick it from under him but instead he appeared to make contact with the 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 quickly ushered away from the tunnel area after the final whistle having been interviewed by police officers.
A Swansea spokesman confirmed no action would be taken, and that Chelsea had invited the 17-year-old, who has been a ball boy at the Liberty Stadium for six years, into their dressing room.
He said: "The police have interviewed the boy and his father and there are no charges going to be pressed, as far as they are concerned that is the matter closed.
"The ball boy has been into the Chelsea dressing room after the game and shaken hands with Eden Hazard. The likes of John Terry and Frank Lampard were exemplary in their behaviour in welcoming him into the dressing room.
"Chelsea asked if he could come in and our kit lady took him in and they shook hands, he is fine.
"As far as we are concerned the matter is closed. He has been a ball boy here for six years with no incidents here at the stadium."