Taking place in the grounds of Harewood House, the festival was a combination of comedy, children's entertainment, sport and food, set up to help the supermarket's charity Raise a Smile reach a target of £500,000 for Save the Children.
Acts due to play included Texas, The Human League, Bob Geldof, Beverley Knight, Soul II Soul, Cher Lloyd, Matt Cardle and Scouting for Girls.
In a statement Morrisons said: "It is with our deepest regret that due to the adverse weather conditions leading up to this event in conjunction with the extreme weather warning as issued by the met office for the weekend, we were left with no other decision than to abandon this weekend's MFEST.
"This was a joint decision made between the promoter, the production team, health and safety and Harewood House. We sought advice from a number of agencies including Leeds City Council before making the decision. The public's health and safety is of paramount concern, therefore it would be irresponsible to continue however disappointed we all are. Information on ticket refunds will be issued on Monday (July 9)."