The sport had already cancelled four races, including the showcase Monaco Grand Prix in May, with a revised and shortened provisional European schedule set to start in Austria without spectators on July 5.
The announcement, widely expected, blew a hole in the long-haul part of the season, with questions about the schedule after Italy's Monza on September 6.
Singapore and Azerbaijan GP organisers said the long lead times needed to build street circuits had made hosting impossible.
"While there are still more than three months to go before the scheduled race on 20 September ... we will be unable to proceed with the race due to the prohibitions imposed on access and construction of the event venue," a Singapore GP statement said.
"Apart from the closure of the event venue, other challenges include ongoing mass gathering and worldwide travel restrictions," it added of the night race.
Singapore has nearly 39,000 COVID-19 cases, one of the highest tallies in Asia due to mass outbreaks in cramped migrant worker dormitories in the city-state.
The race in Baku had already been postponed from June and organisers said they had "explored every possibility" but ran out of time.
Travel restrictions in Japan led to the cancellation of the race at Suzuka on October 11.
The sport indicated some circuits not on the current calendar could now feature instead.
"We have made significant progress with existing and new promoters on the revised calendar and have been particularly encouraged by the interest that has been shown by new venues," the F1 statement said.
A second race in Italy has been mooted for Mugello or Imola, once home of the San Marino Grand Prix, while Germany's Hockenheim and Portugal's Algarve circuit are other possibilities.
Formula One said it expected to publish a final calendar before travelling to Austria. -- Reuters
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