Olympic gatecrasher: India hunts woman in red
The woman, wearing blue trousers and a red top, walked next to India's flag-bearer, wrestler Sushil Kumar.
She stood out in contrast to athletes in yellow saris or blue blazers.
India, already unhappy with its truncated TV coverage during the opening ceremony, is seeking an apology from the London organising committee.
"This was bizarre. We will ask for an apology," India's chef de mission, PKM Raja, told the Times of India.
"The Indian contingent was shown for just 10 seconds and to think this lady hogged all the limelight."
"When we entered the stadium, the woman who was walking between us and the contingent ahead of us, the Independent Olympic Athletes, suddenly came back and started walking next to Sushil Kumar, our flag-bearer.
"We are totally surprised by the manner in which she joined the delegation and kept walking inside the stadium," he said.
He told the newspaper that he was not sure of the woman's nationality.
He said the woman "embarrassed us in front of the world".
Several newspapers claim to have identified the woman in question as a post-graduate from Bengaluru, India. However this remains unconfirmed.
India is fielding 81 athletes at the London Games, with medal hopes in archery, boxing, badminton, shooting, tennis and wrestling.
Olympic organisers Locog have said they will release a statement shortly.