The Kiran MK-II aircraft hit a two-storied building in a residential area near Begumpet airport.
The aircraft was unable to pull up from a dive and went into a spiral as the planes were breaking away from the formation and going in different directions.
The disaster struck when thousands of people were enjoying the spectacle at India Aviation 2010.
The cause of the crash is yet to be determined.
The trainer aircraft was part of the Sagar Pawan Acrobatic Team of the Indian Navy.
According to reports, the plane hit a cell-phone tower and crashed into a three-storey building, which collapsed.
Unofficial accounts say a civilian also died when the plane crashed on the building.
Reports say the HJT-16 Kiran Mk2 trainer was built by Hindustan Aeronautics.