The jet lost contact with other fighters on the flight "minutes before reaching its target area", the Philippine Air Force (PAF) said in a statement.
Air Force spokeswoman Colonel Consuelo Castillo told reporters it was the "first major incident involving" its squadron of FA-50S, which have previously been used in exercises over the disputed South China Sea.
The Philippines has a dozen of the fighters purchased from South Korea in the last decade.
Castillo said the jet was flying "over land" on the way to its target area when it went missing during a "tactical night operation in support of our ground troops".
She declined to provide the exact nature or location of the mission, which saw the fighter flown out of the Mactan-Benito Ebuen Air Base.
The base shares a runway with the airport in Cebu, the Philippines' second-largest city.
"We are hopeful that we will still be able to recover" the aircraft and crew, she said. "We are still very optimistic that they are safe."
In a statement, the Air Force said it was "conducting extensive and thorough search operations, utilizing all available resources, to locate the missing jet fighter aircraft."
The FA-50s have taken part in joint air patrols with treaty ally the United States over the contested South China Sea, where China and the Philippines have been involved in increasingly tense confrontations over reefs and waters.
Beijing claims almost the entirety of the crucial waterway, through which trillions of dollars in commerce transits each year, despite a Hague ruling that its assertion has no legal basis.
Local outlet the Inquirer reported in January that the Philippine government was considering purchasing 12 more FA-50s.
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