The child was born late last night at a hospital here and both the mother and the child are doing well, hospital sources told PTI today.
Soon after, Rajinikanth, 64, paid a visit to the hospital and distributed sweets.
Soundarya, 30, married Ramkumar, an industrialist, in 2010. She directed "Kochadaiiyaan", a motion capture animation movie featuring her father, which released last year.
"I am very happy that both my daughters (Aishwarya Dhanush and Soundarya Ashwin) are making films and at the same time, they have to focus on raising their families (as well). They should not just have children but be with them because they need care up to 10-12 years," Rajinikanth earler said.