Monaco said that the event was "no longer tenable".
The ACM made it clear that the decision was a result of a combination of circumstances, including the potential availability of the workforce required to build up the circuit, along with the volunteers who operate it on the race weekend.
The Historic GP, which was to have taken place a fortnight earlier, has also been cancelled.
The ACM said: "The current situation concerning the worldwide pandemic and its unknown path of evolution, the lack of understanding as to the impact on the FIA F1 World Championship 2020, the uncertainty with regards to the participation of the teams, the consequences with regards to the differing measures of confinement as taken by various governments worldwide, the multi-border restrictions for accessing the Principality of Monaco, the pressure on all implicated businesses, their dedicated staff who are unable to undertake the necessary installations, the availability of the indispensable workforce and volunteers (more than 1500) required for the success of the event means that the situation is no longer tenable.
"As a result, and after careful consideration as to the gravity of this crisis worldwide, it is with great sadness that the Automobile Club de Monaco Board of Directors has taken the decision to cancel the 12th Grand Prix de Monaco Historique and the 78th Grand Prix de Monaco Formula 1.
"To all the fans, spectators, partners and our members, the Board of Directors wishes to express its sincere regrets that these two events cannot be postponed and under no circumstances, will it be possible to organise these events later this year."
Confirmation that Monaco won't be seeking a new slot means that realistically five of the seven races that have already been postponed might potentially be rescheduled.
Last weekend Australian GP organisers admitted that it was highly unlikely that they would be able to hold their race within this season.