The Brazilian saw red after he shoved Alexandre Castro two minutes before the interval and the LFP have ruled that he will now miss the upcoming matches against Lyon and Brest.
With three matches left, PSG top Ligue 1, seven points clear of second-placed Marseille, and they will hope to have the title wrapped up when Silva returns for the final game against Lorient.
The fate of PSG sporting director Leonardo has yet to be decided.
Leonardo is alleged to have pushed the official after the game and the committee will decide what punishment, if any, he will receive at a later date.
He has been suspended as a precautionary measure "due to the seriousness of the offence" and will not be allowed in the dressing room at Lyon next Sunday, the LFP said.
Leonardo insists he was pushed into the referee in the tunnel by the principal match delegate Marc-Gerard Biolchini, an accusation he rejected.
"I didn't barge into or touch Leonardo at any time," he told Le Parisien. "The pictures are clear enough.
"In 20 years I've never known such an act of violence. Already at half-time, Leonardo came to speak to the referee.
"I stopped him going into the dressing room, because he was really annoyed. It's regrettable that it's all ended like this."
Leonardo has already served a suspended two-match ban this season for criticising the referee after PSG defender Mamadou Sakho was sent off in their 1-1 draw at Montpellier in November.