The key manoeuvre was carried out early on Tuesday to slingshot the spacecraft towards the moon.
"Chandrayaan-3 completes its orbits around the Earth and heads towards the moon," the national space agency said, adding, "Next stop: the moon."
"As it arrives at the moon, the Lunar-Orbit Insertion is planned for August 5, 2023," ISRO said.
An ISRO official told PTI that following the trans-lunar injection, the Chandrayaan-3 spacecraft escaped from orbiting the Earth and is now following a path that would take it to the vicinity of the moon.
The ISRO had said it would attempt softlanding on the lunar surface on August 23.
The spacecraft's orbit was progressively increased five times after the Chandrayaan-3 mission to Moon was launched on July 14.