Zaira Wasim, 17, said a "middle-aged man" had repeatedly moved his foot up and down her neck and back while she was "half-asleep".
She documented the incident on Instagram and tried to film the man's behaviour but said it was too dark.
The airline, Air Vistara, said it was carrying out a detailed investigation into the incident.
A suspect has been arrested, Indian media reports say, but his identity has not been disclosed.
