The Interior Ministry said the small plane, a Britten-Norman Islander, was in the Los Roques archipelago, CNN reported. It vanished on Jan. 4 as Missoni flew from the Los Roques airport to Caracas.
There were six people on board, including the pilot and co-pilot and Missoni's wife, Maurizia Castiglioni. No one is believed to have survived the crash.
In a statement to the Italian news agency ANSA, the Missoni family and the families of others on the plane thanked the Italian and Venezuelan authorities for their efforts in finding the wreckage. They said efforts will be made to retrieve the plane.
The Missoni fashion house was founded in 1953 in Gallarte, Italy, by Vittorio's parents. It later moved to Milan and became internationally known for its knitwear.
Ottavio and Rosita Missoni turned over management of the privately owned company to Vittorio and his surviving siblings, Luca and Angela, in 1996. Ottavio Missoni died in May.
A bag was found on Curacao 124 miles from the place where the plane disappeared three weeks later.
Notable deaths of 2014 [PHOTOS]