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The first, run on the official F1 2019 PC video game, will be held from 2000GMT on Sunday when fans should have been tuning in on television to the Bahrain Grand Prix.
The virtual race will be over 28 laps, half the usual distance of the real one under the Sakhir floodlights.
"Every subsequent race weekend will see the postponed real-world Formula One race replaced with a Virtual Grand Prix," Formula One said in a statement.
The Esports Virtual Grand Prix Series will run until May. The season-opening Australian and showcase Monaco Grands Prix have been cancelled along with the races in Bahrain, Vietnam, China, the Netherlands and Spain.
The season is not due to start until the Azerbaijan Grand Prix on June 7, at the earliest.
"The first race of the series will see current F1 drivers line up on the grid alongside a host of stars to be announced in due course," said Formula One, whose existing esports world championship starts later in the year.
"In order to guarantee the participants safety at this time, each driver will join the race remotely, with a host broadcast live from (London's) Gfinity Esports Arena."
The broadcast will be available on the official Formula One YouTube, Twitch and Facebook channels and is expected to run for 90 minutes with qualifying to set the grid positions.
"Due to the wide variety of gaming skill levels amongst the drivers, game settings will be configured in such a way to encourage competitive and entertaining racing," Formula One added.
"This includes running equal car performance with fixed setups, reduced vehicle damage, and optional anti-lock brakes and traction control for those less familiar with the game."
Formula One said it will also host online exhibition races, allowing fans to go head-to-head with real F1 drivers, on non-race weekends.
"We are very pleased to be able to bring some light relief in the form of the F1 Esports Virtual GP, in these unpredictable times, as we hope to entertain fans missing the regular sporting action," said Julian Tan, Formula One's head of Esports.
"With every major sports league in the world unable to compete, it is a great time to highlight the benefits of esports and the incredible skill that's on show."
Formula One will be one of several offerings aiming to fill the gap this weekend, with some Formula One drivers also involved in those.
"Super Sim Saturday" will see three virtual races in quick succession - the Nuerburgring Endurance Series, IMSA Super Sebring and THE RACE All-Stars Esports Battle.
The All-Stars event, first organised at short notice by Torque Esports and www.the-race.com last Sunday when Australia was cancelled and featuring Red Bull's Max Verstappen, has moved from Sunday to Saturday to avoid a clash with F1.
Veloce Esports are also running a 'Not the Bah GP' at 1800GMT on Sunday after an initial 'Not the Aus GP' with McLaren F1 driver Lando Norris last weekend.
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