Sugababe Amelle Berrabah is being treated in a private health clinic for "a severe bout of nervous exhaustion".
A statement on the band's website said that stress over a period of months had taken its toll on the 25-year-old singer.
Keisha Buchanan, who had been the last remaining original member of the Sugababes, left last month in a storm of controversy.
Current members Heidi Range and Jade Ewen said in a joint message on their website that Berrabah will stay in a private health clinic in Europe for three weeks.
She is expected to return to work in full health by the beginning of November.
The statement said: "It seems that, with all the recent events in the band right up to Jade joining us a few weeks ago, the stress over a period of months has unfortunately taken its toll on Amelle and she is now suffering from a severe bout of nervous exhaustion."
Range added: "Both Amelle and I have been through a very traumatic time together in recent months and particularly over the past few weeks.
"Having the opportunity to move forward with Jade was a major factor in us both deciding to carry on as Sugababes.
"And judging from the thousands of well wishes we have received from you, our fans, we are delighted that we made the right decision.
"However, the months leading up to that decision certainly took their toll, especially on Amelle, and it seems like it's now all caught up with her."
The group, who have a new single and album out next month, will be forced to cancel their first live performance together since the line-up change.
They had planned to perform in Leeds and appear on a German TV show this weekend.