A CA spokesman said the Pakistan-born batsman was the only player in Australia's squad not to board because his visa had not arrived in time.
Khawaja posted a popular meme on social media of a man sitting on a garden chair staring into space, with the caption: "Me waiting for my Indian Visa like... #stranded #dontleaveme #standard #anytimenow."
CA expect the visa to arrive later on Wednesday and said Khawaja had been booked on a flight out on Thursday.
Some team support staff are also flying out on Thursday.
India host the first of four tests in Nagpur from February 9th.
Khawaja claimed the Shane Warne award as Australia's men's test player of the year on Monday after a prolific 12 months during which he scored 1,020 runs at an average of 78.46.
