"My daughter Larissa brought a beautiful girl into the world on December 25, 2009," said the 49-year-old German New Wave star, who is set to start a new tour in April.
"The baby is healthy and was born peacefully at home and is called Carla Maria. We are all thrilled about the greatest Christmas gift."
Nena topped charts around the world in the 1980s with the Cold War rock ballad "99 Luftballons", sung as "99 Red Balloons" in English, and went solo after her band of the same name broke up in 1987.
She has had a string of hits in the last decade and still fills stadiums in German-speaking Europe.