Filming on the ITV show was originally due to start this month, but was pushed back three weeks ago due to the third English lockdown and rising cases.
However, on Friday, the talent show's producers said that "safety has to come first" and called it off until 2022.
They said performers like dance groups, choirs and orchestras wouldn't be able to rehearse and audition safely.
The BGT audition shows typically involve hundreds of people congregating and then performing in front of a live audience and judges Simon Cowell, Alesha Dixon, David Walliams and Amanda Holden.
In a statement, the producers said: "Despite everyone at ITV, Thames and Syco doing their best to make it happen, and with our absolute priority of safeguarding the wellbeing and health of every person involved in the programme from judges, hosts and contestants to all of the crew and audience, the decision has been made to - unfortunately - move the record and broadcast of the 15th series of Britain's Got Talent to 2022.
"BGT is known for its diversity of talent with big dance groups, wonderful choirs and lavish orchestras at its heart, and it has become clear that not only is it not possible to film auditions with these types of acts in a secure way but also that they are not able to adequately rehearse and prepare safely.
"Safety has to come first and, as a result, the recording of the show can't currently go ahead as planned."
Filming on the show's latest Christmas special was delayed after at least three crew members tested positive for coronavirus. Last week, Holden said on her Heart Breakfast show there were "still discussions going on" as to whether the next full series would be filmed this year.
In 2020, series 14 was won by comedic pianist Jon Courtenay, with sign-language choir Sign Along With Us finishing in second place.