Six bands were due to compete for a place on the pop group’s 2021 tour, following weeks of pre-recorded audition episodes.
The band – Perrie Edwards, Jade Thirlwall, Jesy Nelson and Leigh-Anne Pinnock – were not among those who tested positive.
— Little Mix The Search (@LMTheSearch) October 14, 2020
The BBC One talent show sees the former X Factor winners create and mentor new bands.
Its live show is now expected to air on Saturday October 24, the same date as Strictly Come Dancing’s first live show of the series.
A statement from the BBC said: “We can confirm that a small number of people on the Little Mix The Search production have tested positive for coronavirus and they are now self-isolating following the latest Government guidelines.
“Due to the format of the show we have made the decision to postpone Saturday’s programme.
“There are rigorous protocols in place to manage Covid-19 as the safety of all those involved in the production is paramount.
“We hope to be back on air on Saturday October 24.”
It was previously announced that comedian Chris Ramsey will host the programme.
Little Mix recently announced details of their sixth studio album, Confetti, due for release on November 6.
They formed on The X Factor in 2011 and have become one of the country’s biggest-selling girl bands.