The twin-engine police jet was en route to the island of Batam near southern Singapore.
The plane set off from Pangkal Pinang, Bangka Island in the direction of the Riau Islands, before crashing into the water at around 10am.
Debris from the M-28 Skytruck was found by fishermen on the coast of Pulau Senayang, Riau Islands province, at 11.30am local time.
Authorities believe the plane may have gone down between the islands of Mensanak and Sebangka or Gentar.
A search team has recovered items which are believed to belong to the missing aircraft.
12 passengers are feared dead.
“An explosion was heard before the plane crash. Pieces of chairs and bodies were found by residents,” Tanjung Pinang naval base commander First Adm. S. Irawan told The Jakarta Post.
The Commander confirmed that the Navy launched three naval warships and three patrol boats to assist in rescue attempts.