The decision to punish the principality club was taken by the Ligue de Football Professionel following crowd trouble at the game against Le Mans on May 17.
The LFP released a statement outlining the reasons behind the sanction, saying it was due to "the behaviour of supporters: the use of pyrotechnics, encroachment on to the field of play at the end of the game and the aggression shown towards the referee by a spectator".
The full punishment was three points but one was suspended while Monaco must also play their first home game of the season, scheduled to be against Montpellier on the weekend of August 16/17/18, behind closed doors.
The news is a significant blow to the Monte Carlo club, and ambitious Russian owner Dmitry Rybolovlev.
Rybolovlev bankrolled Monaco's return to the top flight under coach Claudio Ranieri and has already invested heavily in the likes of Radamel Falcao, James Rodriguez and Ricardo Carvalho this summer.