It crashed into a building that was under construction in Ghatkopar, a residential area in eastern Mumbai.
Fire officials told BBC Marathi that the dead included four people on the flight and one person on the ground.
Initial reports say the plane crashed while the pilot was attempting to land. It burst into flames immediately after.
The plane was sold to a private individual by the government of the northern state of Uttar Pradesh, a senior police official told the BBC.