Some 14 policemen complained that money was withdrawn from their bank accounts with Indian bank Axis through ATM machines in Greece as well as in Mumbai, broadcaster NDTV reported.
"There has been a complaint from Axis bank that some scheming has been done in 29 accounts. We are in the process of registering a complaint and we will investigate the matter," senior police officer Satyanarayan Chaudhary told reporters.
A total of 1.3 million rupees (22,600 dollars) was stolen, NDTV said.
Police suspect the debit cards of policemen were cloned, the report said.
Voice of Russia, dpa