The bronze cannon, from the late 15th century, bears a striking resemblance to sketches drawn by the Renaissance inventor, notably in his Codex Atlanticus - the largest collection of his drawings and writing.
Mounted on a wooden carriage and wheels, it would have allowed a much more rapid rate of fire than traditional single-barreled guns - in a precursor to modern day machine guns. Soldiers would have been able to fire three cannon balls instead of one.
It was also lighter and more mobile than most cannon of the time, enabling troops to move it around the battlefield with comparative ease - a precursor to much later artillery.
It was found in the grounds of the 15th century Klicevica fortress, in a part of southernCroatiathat had strong trading links with the Venetian Republic and that was on the front line of defence against the invading Ottomon Turks.
"We think it was either made in Venice and brought here, or it may have been made locally," said Marin Curkovic, the director of a museum in the nearby town of Benkovac, where the cannon went on display this week as the centre-piece of a new exhibition.
"We cannot say with 100 per cent certainty that it was built to Leonardo da Vinci's designs but the resemblance to his sketches is remarkable. We think there is a very high probability that it was manufactured to his designs."
The weapon almost exactly matches a model of da Vinci's triple-barrelled cannon design, which is on display in the Leonardo da Vinci Museum of Science and Technology in Milan.
The cannon may not have been an enormous success - the lower part of the barrels has been blown away, suggesting it may have jammed and exploded, probably killing or seriously injuring whoever was operating it.
The gun was found in 1968 by a group of children who were digging in the fortress, but it was only donated to the museum in the 1990s.
Attempts to properly analyse it were stymied by Croatia's war of independence and a lack of funds.
"There are no markings on the cannon so it was hard to date it until we were able to excavate the area where it was found and start putting it into some sort of context," said Tomislav Basic, also from the museum.
"As far as we know, it is unique in the world. Nobody else has found anything like it. It's a very exciting discovery."