Two other soldiers were injured, it said in a statement, adding the army retaliated by hitting specified targets.
The ministry did not give further information.
A Russian-backed Damascus offensive on the last rebel bastion in the country has killed hundreds of civilians since December and displaced close to a million people.
A ceasefire between rebel-backer Turkey and regime-ally Russia was agreed for Idlib and came into force on March 6.
However Russian air strikes hit Idlib on Tuesday and Wednesday, the first attacks since the ceasefire agreement.
Some 840,000 of the nearly one million remain displaced, while some 120,000 have returned to their home communities since the ceasefire went into force, according to the United Nations.
The truce, which coincided with the coronavirus crisis, had put a stop to the relentless air strikes by regime forces and their Russian allies that killed at least 500 civilians in four months.
Late last month, a Turkish soldier was killed by a roadside bomb while on patrol on the key M4 highway in Idlib.
Nearly half of the three million people living in the Idlib region have been displaced from other parts of Syria recaptured by the government.
After holding barely a fifth of the country five years ago, Russian intervention has helped the government reclaim control of more than 70 percent of Syria.