United executive vice chairman Ed Woodward held an emergency meeting with Premier League executive chairman Richard Scudamore before deciding to call-off the game.
Now both clubs must decide when to play the re-arranged fixture, which carries valuable prize money as well as league points.
One option is for it to take place tomorrow behind closed doors because there is no time to organise the policing of the game.
United face Crystal Palace in the FA Cup next weekend and would want to face the Cherries before Wednesday.
To complicate matters further, the Europa League takes place on Wednesday night and England face Turkey at the Etihad on Sunday.