Named Karys Koh, the newborn awaits a Chinese name.
Ms Lee and her husband, telecommunications consultant Jacky Koh, are still "cracking our heads" to decide on Karys' Chinese name, she wrote in English on her Facebook page yesterday.
The baby, like her mother who turns 36 this month, is born in the Year of the Horse.
Ms Lee, the MP for Punggol East, posted on Facebook a picture of her child hours after her delivery at Mount Alvernia Hospital.
Writing in Mandarin, she said: "After going through an unstable pregnancy, enduring frequent pregnancy rash, and after nine months of waiting, we finally welcomed our daughter's arrival today!"
She also wrote in English that "like many mothers, I will have many challenges to face as well and, like them, I will persevere to get through these obstacles!"
Ms Lee is the second MP to give birth in recent years. Minister of State Sim Ann, who is an MP for Holland-Bukit Timah GRC, had her third child in 2011.
According to a Facebook post by her husband, Ms Lee worked until the eve of her delivery, turning up for her Meet-the-People Session (MPS) on Monday night.
During her confinement period, both WP chief Low Thia Khiang and Hougang MP Png Eng Huat will take turns to cover her MPS duties, she told her constituency members.
On her Facebook page yesterday, Ms Lee thanked the residents who had given her their best wishes and advice during her pregnancy.
She also encouraged people to donate to the Singapore Cord Blood Bank, after donating her daughter's umbilical cord blood. This, she said, would help anyone requiring stem cell therapy.
Ms Lee won the Punggol East by-election in January last year and a year later, shared news of her pregnancy.
As a full-time MP, she has spoken on the challenges faced by working mothers and the need for policies to help them strike a better balance between work and family life.
This article was first published on JULY 2, 2014.
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