It has also been revealed that Nelson, 29, will not be performing at the MTV European Music Awards on Sunday (8 November).
A representative for Little Mix said: “Jesy is unwell and will not be appearing on tonight’s final of Little Mix The Search.”
“She will also not be hosting or performing at tomorrow’s MTV EMAs.”
The Search, which is broadcast on the BBC, follows six new bands as they compete to join Little Mix on their next tour.
The news comes soon after Nelson was said to have looked “over it” in a promotional video for the band’s new record, Confetti.
According to fans, the singer looked far less enthusiastic than her bandmates Leigh-Anne Pinnock, Perrie Edwards and Jade Thirlwall.
The clip proved so controversial on social media that it was deleted from music platform Anghami’s official Twitter page.
Nelson was last seen on Friday night’s edition of The Search (6 November), which was delayed from last Saturday (31 October).
The Independent’s Roisin O’Connor called Little Mix’s new album “a glamorous statement of independence