Monaco were handed a three-point penalty, with one suspended, after the trouble at their final home match of last season at Stade Louis II on May 17.
The title celebrations were marred by fans lighting flares and a pitch invasion after the final whistle, during which the referee was attacked by a supporter.
The club will also have to play one game behind closed doors.
"Regarding the seriousness of the facts, Monaco are condemned to one match behind closed doors and a three-point penalty, including one suspended, for the next Ligue 1 season," the LFP said in a statement.
The sanction is a heavy blow to Monaco, who are expected to challenge defending champions Paris Saint-Germain, after marking their return to the top-flight with several big signings, including that of Colombian striker Radamel Falcao from Atletico Madrid.