The crash involved two L-410 Turbolet sport airplanes with 38 people on board, most of them parachutists preparing for an air show, according to Zuzana Farkasova from the interior ministry's firefighters division.
The seven dead included four pilots and three parachutists, according to local media.
Five parachutists walked away with minor injuries after the planes crashed near the village of Cerveny Kamen near the Czech border, according to health ministry spokesman Peter Bubla.
However, most of the survivors were able to parachute out of the aircraft immediately after the crash, a police source told AFP.