Hazard was sent off after an altercation with 17-year-old Charlie Morgan, who appeared to lie on top of the ball during Chelsea's Capital One Cup semi-final second leg against Swansea.
The FA charged Hazard over the incident, alleging that the standard three-match ban for violent conduct was "clearly insufficient". However, Chelsea convinced an independent regulatory commission not to increase the sanction.
An FA statement said: "Following a hearing earlier today, an independent regulatory commission was of the opinion the existing three-match sanction for this offence was sufficient.
"The FA 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 denied the charge and the matter was dealt with at a non-personal hearing.
"The FA will be reminding all clubs of their responsibilities in ensuring ball boys and other personnel around the pitch act in an appropriate manner at all times and The FA will be liaising with competitions accordingly."
Hazard has already missed games against Brentford and Reading, and will serve the final part of his ban against Newcastle on Saturday. He will be eligible to play against Wigan on Saturday, February 9.
Prior to the decision, Chelsea manager Rafa Benitez said: "For a player that was in a cup competition, with this intensity and in the way that things are going on, I think that a three-game ban is enough.
"I have a lot of images but I think that, for a professional, and for the club, we have already lost the player at the end of the game, we will lose the player at least for three games. I think it's enough."