"The baby was born late on Wednesday night. Both -- the baby and the mother -- are absolutely fine," said a source close to Rajini.
Soundarya married Ashwin Ramkumar, an industrialist, in 2010. This is the couple's first child.
Soundarya is best known for directing India's first motion capture animated film Kochadaiyaan, featuring her father.
At the audio launch of Kochadaiyaan in 2013, Rajini publicly wished for his daughter Soundarya to settle down and subsequently chase her filmmaking dream.
Rajinikanth already has two grandsons, Yatra and Linga, from his second daughter Aishwarya, who is married to popular actor Dhanush.
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