The Monsters were scheduled to play the Grand Rapids Griffins at Rocket Mortgage FieldHouse at 7 p.m.
All tickets will be honored for a rescheduled game yet to be announced.
The promotion and giveaway planned will be rescheduled as well.
Their National Hockey League affiliate, the Columbus Blue Jackets, is also seeing some games postponed.
The Blue Jackets were scheduled to play in Chicago Tuesday.
The league announced other big changes so teams could fill their roster with enough players as more people go into COVID-19 protocols.