The white-coloured bird was found by a local resident in India's Punjab state, which borders Pakistan, and taken to a police station 25 miles from the capital Amritsar.
The pigeon had a ring around its foot and a Pakistani telephone number and address stamped on its body in red ink.
Ramdas Jagjit Singh Chahal, a police officer, said he suspected that the pigeon had landed on Indian soil from Pakistan with a message, although no trace of a note has been found.
Officials have directed that no-one be allowed to visit the pigeon, which police say may have been on a "special mission of spying".
The bird has been medically examined and was being kept in an air-conditioned room under police guard.
Senior officers have asked to be kept updated on the situation three times a day, according to a report from the Press Trust of India (PTI) news agency.
Mr Chahal said local pigeon fanciers in the sensitive border area had told police that Pakistani pigeons were easily identifiable as they look different from Indian
ones, according to the Indian Express newspaper.
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how are they going to sentence a pigeon if found guilty to hard labour?