Poulumi, daughter of IAS officer Pradeep Shukla, was apprehended after an airline official flagged discrepancies in the visa on Wednesday, they said. Shukla is an accused in the NRHM scam in Uttar Pradesh.
The girl, who was carrying two passports, including an expired one, had allegedly superimposed a copy of US visa on one of the pages of her passport. The expired passport had a valid visa sticker.
Poulumi was to board an Air India flight to New York on Wednesday.
Police sources said she was "uncooperative" during questioning.
After expiry of her passport, a new one was issued in August last year. The expired passport had a genuine US visa, which was valid till 2019.
Police sources said they could not ascertain why she appended a fake visa when she actually had a valid visa.