The LFP's disciplinary committee handed down the punishment for the incident which occurred during a match at home to Valenciennes on May 5 after meeting yesterday with Leonardo and officials from the match.
The Brazilian was alleged to have barged into referee Alexandre Castro after the game and has since been provisionally suspended.
And the LFP confirmed on its official website it had now suspended him for nine months, with the ban keeping him from "the touchline, the referees' dressing room and all official functions".
PSG reacted angrily to the punishment, and have decided to appeal against the ban.
The club released a statement which read: 'Paris St Germain takes note of the decision of the LFP disciplinary committee to suspend Leonardo, the team's sporting director, for a nine-month period and to sanction the club by a conditional withdrawal of three points.
'In the light of the material elements submitted to the members of the disciplinary committee, Paris St Germain considers this decision to be unjustified and extremely harsh. As a result, and in solidarity with their sporting director, Paris St Germain will appeal this decision.'
Leonardo had claimed he was pushed into the referee in the tunnel by the principal match delegate Marc-Gerard Biolchini, but the disciplinary committee decided the action was deliberate.
The 43-year-old can appeal the punishment.
Leonardo has been outspoken of his criticism of referees this season and described the sending-off of defender Thiago Silva in the match as "unacceptable".
The French champions have also been handed a suspended three-point deduction for next season.
'I'm happy to have been heard,' Leonardo, who won the World Cup as a player with Brazil in 1994, told reporters. He was speaking after his hearing but before finding out the punishment.
The ban, which rules the sporting director out for most of the coming season, is a further blow to the capital club, who appear to have a fight on their hands to keep hold of coach Carlo Ancelotti.
The Italian, who has a year left on his contract, is attracted by the Real Madrid job, but PSG's wealthy owners are unwilling to let him go.