As the government is keeping most hygiene and social distancing measures in place for now, it is impossible to consider holding an event on such a scale, a statement said. The two-week festival along Lake Geneva draws nearly 250,000 people.
"The programme planned for this summer will be partly carried over to next year’s festival, which will take place from 2 to 17 July 2021," it added.
Lionel Richie and Lenny Kravitz were among those booked to play this year, it said.
Last year's eclectic line-up featured Elton John, Sting, Janet Jackson, Chick Corea and Radiohead frontman Thom Yorke.
Veteran American producer Quincy Jones, a former co-director of Montreux who still participates each year, calls it the "Rolls-Royce of festivals".
The festival joins a long list cultural events that have been cancelled or postponed because of lockdowns and measures to prevent the spread of the coronavirus, including concerts, festivals and book fairs.