The sister events will next take place from 15 to 20 June 2021.
"Over the last few months, we have been closely monitoring the Covid-19 situation," said Jennifer Roberts, CEO of Design Miami.
"In line with current recommendations from the Swiss government and to protect the health and safety of our exhibitors, partners, employees, and visitors, Design Miami/ has made the difficult decision in conjunction with Art Basel not to proceed with the postponed September 2020 edition of the Basel fair."
December fairs to go ahead
The December editions of Art Basel and Design Miami, held in Miami Beach in Florida, are currently still due to go ahead from 2 to 6 December.
The events join other September events that have been cancelled or postponed including Frankfurt lighting show Light + Building, and London Design Biennale and London Design Fair.
Light + Building cancelled
Frankfurt's giant Light + Building fair, which is usually held in February, was moved to September in the hope that the pandemic would have eased by then.
However, organisers announced last month that the biannual fair will not take place at all this year. The next Light + Building fair will be held from 13 to 18 March 2022.
Other events that have announced changes to their plans in the past week include Jerusalem Design Week and the Architectural Digest Design Show.
Jerusalem Design Week postponed
Jerusalem Design Week, originally slated for 18 to 26 June 2020, has been postponed until further notice. New York's Architectural Digest Design Show was first moved from March to June but has now been cancelled altogether.
Fairs and festivals that are still due to go ahead this month include Reykjavík's rescheduled Design March, now taking place from 24 to 28 June, and San Francisco Design Week, which will take place entirely online from 16 to 25 June.
Some autumn events still taking place
Events still scheduled for September include Design China Beijing, Helsinki Design Week and London Design Festival, although festival components the London Design Biennale and London Design Fair have been postponed.
October's Dutch Design Week will still go ahead but in a much reduced physical form, with most activities taking place online.
See an up-to-date list of architecture and design events at Dezeen Events Guide, which has a special page dedicated to fairs impacted by Covid-19.
Photography is by James Harris.