The Russian-made fighter aircraft Su-22M4 were believed to crash into the East Sea about six nautical miles from Phu Quy Island.
Air controllers lost contact with the pilots at around 10:40 a.m.
So far rescuers have found three oil barrels and pieces of a parachute. Traces of oil were also spotted near the accident site.
Initial information is that the 1976-produced aircraft were part of a team tasked with protecting the Truong Sa (Spratly) Islands.
The search and rescue mission is going on.
On March 26, a military helicopter, also produced during Soviet ear, crashed when it was about to land on Phu Quy Island, but all men all board survived.
Two previous crashes involved a Russian Mi-171 and a US-built UH-1, and killed 24 military personnel in total.
The Vietnam People's Air Force Su-22M4. Su-17M-4 ('Fitter-K') attack aircraft.