Srija married Sirish Bharadwaj, an engineering graduate, at the Arya Samaj ashram in New Bowenpally in Secunderabad and later the couple disappeared.
A few friends of the couple attended the simple ceremony, which shocked the family of the Telugu superstar.
Chiranjeevi, one of the highest paid actors in India, had reportedly opposed Srija's choice prompting her to marry her love without the consent of the family.
The marriage was also telecast live by a Telugu television channel. Srija told reporters that she was in love with Bharadwaj, a resident of Hyderabad, for the last four years.
"Today morning I escaped from home and we got married. It is a legal marriage as I am 19 and he is 22," she said.
The bride added she also loved her father and hoped he would approve the marriage. The couple said they would meet Chiranjeevi to seek his blessing but did not turn up at his residence in the upscale Jubliee Hills till this evening.
The superstar's family has been in news for a while.
The marriage of the actor's elder daughter Sushmita with actor Uday Kiran was cancelled at the last minute when Chiranjeevi's family learnt that the groom was in love with another girl. Sushmita last year married a businessman from Chennai.
Chiranjeevi's younger brother Pavan Kalyan has been in news for a bigamy case filed against him by his wife Nandini in a Visakhapatnam court. Alleging that Pavan had married actress Renu Desai without divorcing her, Nandini has demanded compensation from the actor.