The wreckage of the Junkers Ju 87 or Stuka (Sturzkampfflugzeug) 'dive bomber' was discovered not far from the southern coast of the island of Zirje, institute official Igor Miholjek told AFP.
Only two bombers of that type, out of some 5,700 that were produced, have been preserved and are now on show in London and Chicago, according to the institute.
The plane was found around 28 meters down during a diving trip organized by the institute, in which Miholjek took part.
"The engine, which was most likely ripped off when the plane hit the water, was missing and was found nearby, but the rest of the aircraft is complete and in very good condition," he said.
"The plane is lying on its wheels as if it smoothly landed on the seabed," he said, adding that it was still unclear when it would be recovered.
The bomber was most likely an Italian plane hit by Yugoslavia's navy in April 1941 during the invasion by the German-led Axis powers at the start of the Second World War.
Two more had been found in the sea waters of Norway and Greece, but apparently in much worse condition that the one near Zirje, which is some 340 kilometres south of Zagreb.
It is the second Second World War plane found almost complete in Croatia's Adriatic.
The first, a B-17 Flying Fortress, was found in 1998 in the waters of the southern island of Vis but was not recovered.
'Stuka' bombers were designed for a dive-bombing technique which consisted of diving on the target at a steep angle and releasing the bombs at a low altitude for maximum accuracy.