A rep for Little Mix said: "Jesy is having extended time off from Little Mix for private medical reasons.
"We will not be issuing any further comment currently and ask media to please respect her privacy at this time."
Earlier this month, Jesy sparked concern amongst Little Mix fans after pulling out of the final of BBC series Little Mix: The Search.
Jesy also was unable to attend the 2020 Europe Music Awards where Little Mix had been booked to host and perform during the evening.
Despite Jesy's absence, Perrie Edwards, Jade Thirlwall and Leigh-Anne Pinnock continued to perform and host the show.
A statement at the time read: "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 same weekend Little Mix released their sixth album Confetti.
The record debuted at number two in the UK charts last week, narrowly being pipped to the top spot by Aussie superstar Kylie Minogue.
The girls did however hit number one in Ireland.
Jesy also didn't appear in a pre-recorded Little Mix sketch with children's TV duo Dick and Dom on Children In Need which aired last Friday.
Earlier this week, fans of the chart-topping band expressed their concern after signed albums they had ordered online arrived without Jesy's signature.
After news of Jesy's extended departure broke, fans of the starlet flocked to Twitter to express their sadness and share their well wishes.
One fan wrote: "Jesy Nelson I love you Red heart Take all the time you need."
Another added: "Sending all my love to Jesy Nelson."
A third continued: "Jesy Nelson we love you."
"Sending huge love to Jesy Nelson and Little Mix. Hope she comes back when she’s ready."
A fourth replied to the statement saying: "Please send her all our love, I hope she get well soon. We love you Jesy Nelson."
Jesy won The X Factor as part of Little Mix in 2011.
They were guided to success by mentor Tulisa Contostavlos.
Since then the group have sold over 50 million records around the world.
In 2018 Little Mix parted ways with Simon Cowell's record company SyCo.
The group moved to rival record label RCA – also under the Sony Music umbrella – amid report Cowell clashed with Little Mix's management company Modest.
Playing down reports of a major rift, Cowell told The Sun at the time the move had nothing to do with money.
The X Factor bosses said: "Basically, they said we'd done a terrible job.
"I had agreed not to talk about this publicly because I thought it was a private matter.
"I said 'We can't work with the management, it's as simple as that'."