Hazard was sent off for violent conduct following the incident at the Liberty Stadium, in which he tussled with ball boy Charlie Morgan after the youngster refused to give him the ball.
The Belgian's red card generated an automatic three-match suspension, but subsequently the FA suggested this was "clearly insufficient" and looked at an additional charge.
However, an FA statement issued on Thursday said: "Chelsea player Eden Hazard will not have his standard three-match sanction for violent conduct increased.
"Following a hearing earlier today, an independent regulatory commission was of the opinion the existing three-match sanction for this offence was sufficient."
Hazard, a close-season signing from Lille, missed Chelsea's draws against Brentford and Reading but will be available for next weekend's home game against Wigan, which follows this weekend's trip to Newcastle.
Although some within football thought Hazard over-reacted, others were more sympathetic and pointed out how Morgan, the son of a Swansea director, had tweeted his intention to waste time ahead of the match and had prevented the Chelsea playmaker from retrieving the ball by lying on it.
And in a bid to prevent a repeat incident, the FA statement added: "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."