The 60kg calf named Bonnie was born at the park, near Stirling, following a 16-month pregnancy.
Keepers said the birth marked an important step in the work to save the species from extinction.
Southern white rhinos, native to the south of Africa, are currently listed as near-threatened on the IUCN red list of endangered species.
The calf is the fifth to be born at the park to mother Dot and father Graham, both aged 16.
Animal collection manager Sheila Walker said: "The birth was very straightforward and the calf was up on its feet and suckling in just over an hour.
"Dot is a great mum and very experienced, having successfully raised four calves previously. She was even giving gentle nudges, encouraging the calf to its feet - but it managed all by itself, albeit a bit wobbly at first."
Despite its endangered listing, the white rhino has fared far better than its northern counterpart, which was declared extinct in the wild in 2008. About 18,000 southern white rhinos remain in the wild.
The animal's decline has been blamed on poaching in Africa. Blair Drummond said it was committed to doing its bit to help save the species from extinction.
Ailsa McCormick, head keeper of the park's large mammals, said: "The calf is of big importance to the endangered species breeding programme, and I'm delighted to oversee Dot and Graham's continued part in ensuring a strong viable insurance population for southern white rhinos.
"This calf is their fifth, and being grandparents at 16 years old, Dot and Graham's latest calf is a big feather in the cap for the ongoing conservation efforts made by Blair Drummond."
The park said it had been receiving messages from well-wishers after people viewed the birth live via a webcam.
A southern white rhino has given birth to a female calf at Blair Drummond Safari Park.