Search teams have found plane wreckage at around 6:00 a.m. local time (00:00 GMT) and later discovered two bodies at the site, the ministry said, according to the news outlet.
The identities of the victims have not been disclosed.
On Saturday, a small private plane with five German citizens on board went missing after departing from Mexico off the coast of Costa Rica, Costa Rican Public Security Minister Jorge Torres said. Later in the day, German newspaper Bild am Sonntag reported that passengers included the CEO of the largest fitness club chain in Germany McFit, Rainer Schaller, with his girlfriend and two children, and a man named Marcus Kurreck.