The chart-toppers were singing Down And Dirty when singer Perrie Edwards went off script.
"F*** that Get Down And Dirty", she shouted down her microphone, causing Radio 1 to cut its live broadcast from the main stage.
Radio 1 DJ Matt Edmondson told listeners, and viewers watching the live broadcast on the iPlayer: "Apologies there. Sincere apologies for any bad language you might have heard."
He added: "That was not intended to go out on the radio. We apologise if you're offended by that. We're doing to dip out of their set for a little while now."
Instead, Radio 1 played a Justin Bieber track, with Edmondson saying "rather conveniently" it was the Canadian singer's 2015 single Sorry.
Earlier the Shout Out To My Ex singers had been hit by costume trouble when Jade Thirlwall's trousers split, possibly delaying Little Mix's journey to the stage.
"They were warming up and doing a little dance routine, and Jade's pants split," DJ Cel Spellman said.
Edmondson added: "Her trousers split right down the side, so she's been furnished with some new ones."
The band, Jesy Nelson, who showed off a new, blonde hairdo, Leigh-Anne Pinnock, Edwards and Thirlwall, opened Sunday's festival slot in Hull with Power and sang their hits like Black Magic.
Last night Katy Perry led tributes to the victims of the Manchester bombing at the event, telling the crowd "we're all in this together".
The US singer dedicated a performance of Part Of Me to the people of Manchester over the attack on those leaving Ariana Grande's pop concert.
"We will still dance, we will still sing, we will still make music", she said.