Those behind the annual event - which attracts 150,000 spectators and contributes millions to the city's economy - said the decision was made with a "heavy heart" after taking into account the "enormous" demand the Chapeltown carnival will have on council staff, blue-light services, designers and others.
In a statement officially announcing the decision, carnival chairman and founder Arthur France said: "As carnivalist, we know how to unite the city through joy, happiness and adversity and it’s these qualities that will help us get through these difficult times.
"We will be back in 2021 bigger and better with an array feathers, gems, sequins, costumes and music.
Lamborghini pictured with car on top of its bonnet at busy Leeds junction following crash
Rage Against The Machine pull out of headline slot at Leeds Festival
Leeds Bradford Airport: Full statement on August security staff strike
Teenager arrested in Leeds as part of firearms offences probe
Crack-addicted shop robber claimed pal borrowed his clothing
"I would like to thank everyone involved in carnival over the last 53 years and especially the carnival committee who given up their time for the love of carnival.
"We support our long standing partner, our friends at Leeds City Council and together we’ll be jammin' again."
The carnival was due to be held on Monday August 31 and organisers had previously said they were closely monitoring the situation.
But on Sunday, a full statement was released, together with Leeds City Council, to announce its cancellation.
Leeds City Council Leader Coun Judith Blake said: "Carnival is a wonderful and integral part of what Leeds is all about.
"It’s a living representation of the heart and soul of the city and as the oldest West Indian Carnival in Europe it is one of the most important events in the national cultural calendar.
"We really appreciate the carnival committee’s commitment and their understanding of the pressures of this very difficult and unprecedented situation and we will be working with them to find a way of using the grant funding we give to this wonderful, spectacular and unifying event that makes the most of its incredible ability to bring communities and people together."
Coun Mohammed Rafique, executive member for environment and active lifestyles, acknowledged many will be disappointed by the announcement but it was the "best thing to do" under these "extraordinary circumstances" to ensure the safety of the 150,000 spectators who flock to the city each year.
He added: "It’s one of the greatest annual events in Leeds bringing people of all backgrounds together in a celebration of love, culture and community participation on so many levels and we very much look forward to the next event."