At birth, the baby girl weighed 2.82 kilograms and is 46.5 cm long.
Gibran was reluctant to reveal the name he had saved for the infant, as he was awaiting the arrival of his father, President Jokowi, in Surakarta.
President Jokowi had earlier stated, in a separate instance, that he continued to monitor the developments after the birth of his third grandchild.
He also gave all authority of naming the baby to his eldest son.
First Lady Iriana had accompanied her daughter-in-law, Selvi Ananda, moments before labour to the PKU Muhammadiyah Hospital, it was reported.
She was nervous while waiting for her daughter-in-law to give birth through a caesarean section, she revealed.
President Jokowi is now a grandfather to three grandchildren. His other grandchildren, before this newborn, are Jan Ethes Sri Narendra, the firstborn of Gibran Rakabuming Raka and Selvi Ananda, and Sedah Mirah from Kahiyang Ayu, his daughter, and Bobby Nasution.
Related news: President Jokowi welcomes first grandson
Related news: Jokowi`s eldest son Gibran, Selvi officially married