Indian Exit Visa
If you are a U.S. citizen and if your passport is lost or stolen while in India, you must first contact the U.S. Embassy/Consulate in India who will issue a replacement passport. However, you will have to get an exit visa stamp in your passport before Indian authorities will allow you to leave India.
This exit visa allows the traveler a specified period of time (usually a few days) in which to leave the country legally. No fee is charged for an exit visa. Only applicants seeking to extend their Indian visa must pay a fee.
Please keep in mind that while you are in India, you are subject to Indian laws, regulations and procedures.
You need to get an exit visa at the Foreigners Regional Registration Office (FRRO).
In order to get an exit visa, you need to submit the following documents:
Your replacement U.S. passport.
The letter issued by the U.S. Embassy/Consulate giving the details of your lost or stolen passport.
Original police report.
A letter from the airline on which you arrived verifying the date and place of your arrival in India or your original boarding pass.
If you have a copy of your Indian visa and entry stamp, that may facilitate the process of applying for an exit visa.
U.S. Embassy/Consulate is unable to intervene in routine requests for exit visas from the Government of India. FRRO would be in the best position to advise you on how long the process will take.