The 15-minute show will debut in June. It follows the cast of a play who continue to rehearse remotely after their upcoming West End production is suddenly brought to a halt because of the coronavirus pandemic.
"Absurd and humorous in equal measure, Staged takes on the challenges of creating a drama in lockdown, on stage and off, with a line-up including Georgia Tennant, Lucy Eaton and Anna Lundberg," a BBC press release said. "The show will also have a selection of guest stars including Nina Sosanya, with more to be confirmed in due course."
Simon Evans and Phin Glynn came up with the idea and Evans penned the screenplay.
It will be recorded using video-conference technology in keeping with social-distancing practices.
"It's vital that the BBC provides moments of light relief and this mischievous idea shows what great sports Michael and David are in sending themselves up," Charlotte Moore, director of BBC Content, said in a statement.