The 34-year-old shared the news of her newborn's arrival on Instagram yesterday, writing: "Welcome to the world little Luna".
This is Missy's second child with her partner comedian Dan Lee, who she has been married to since 2016.
They currently share a three-year-old son, Samuel Arrow Lee, who she gave birth to in 2015.
Missy announced her second pregnancy in March this year when she took to the stage as Ed Sheeran's support act.
"I wanted to write a song that kind of put the day I met Dan into a song so I could play it for our children," she said to the crowd.
"And on that note, I'd like to tell you guys that I'm expecting.
"This is the first time I've ever said it publicly. So there you go, that's what this little bump's doing down here."