Major general Ido Nehushtan, the Israeli air force commander, called an official inquiry and halted training in Israel's F-16 squadrons "until further notice" the military said in a statement.
Asaf's father Ilan was one of seven crew members killed in the Columbia shuttle when it exploded shorlty before landing.
A former fighter pilot who took part in Israel's bombing of the Iraqi nuclear reactor in 1981, he was the payload specialist on the shuttle flight.
The space shuttle Columbia broke apart about 20 km over Texas as it headed for landing on February 1, 2003.
Seven astronauts - six Americans and Ramon - died after spacecraft's heat shield suffered damage caused during its launch two weeks earlier.
His son, the oldest of his four children, graduated from a flight school in June.