The detainee has been identified as Shivkumar Sahane, DCP (Zone VI) Sangramsingh Nishandar said, adding, two more detentions are likely in the case.
Three people were seen using a remote-controlled drone flying at a height of around 55 feet yesterday, the official said.
"The drone flew for nearly 25 minutes over the BARC campus at Trombay, an eastern suburb of Mumbai," he said.
A professor who happened to see the drone videographed the incident on his mobile phone and submitted it to the police, the police official said.
He said that that the professor who was passing by is an eye witness in the case.
After photographing the BARC campus, the trio fled the spot in car, the official said.
A case has been lodged at the Trombay police station and the police located Sahane with the help of the professor's video recording, after which he has been detained for questioning, he said.
The detainee told the police that the BARC campus was photographed to upload it on the property website, the DCP said.
The police has not made any arrests so far but the trio are likely to be booked for using drones without having permission from authorities concerned or the police, he added.