The Syrian military said facilities in Hama and Aleppo provinces were struck.
It did not immediately report any casualties. But a UK-based monitoring group said 26 pro-government fighters were killed, most of them Iranians.
It is not known who was behind the attacks. Western nations and Israel have previously hit sites in Syria.
Earlier this month, the US, UK and France bombed three facilities they said were associated with the Syrian government's alleged chemical weapons programme.
Israel is meanwhile alleged to have hit an airbase in Homs province reportedly serving as an Iranian drone command centre and containing an advanced Iranian air defence system.
Seven Iranian soldiers were among 14 military personnel killed in that attack.
Israel has repeatedly vowed to stop its arch-enemy Iran from strengthening its military presence in Syria, Iran's closest ally.
A Syrian military source cited by the official Sana news agency said only that the sites targeted on Sunday night were "exposed… to a new aggression".
The source added that the strikes came after terrorist organisations had suffered defeats in the countryside of the capital, Damascus, an apparent reference to the recent recapture of the Eastern Ghouta region from rebel groups.
The Syrian Observatory for Human Rights (SOHR), a UK-based monitoring group, said the attack appeared
to have targeted a surface-to-surface missile depot at the 47th Brigade military base, south of the city of Hama.
The pro-opposition Orient News website also reported that large explosions were seen coming from what were believed to be ammunition caches at the base.
Missiles are also reported to have hit locations in the Salhab area, west of Hama city, and the area surrounding Nairab military airport, which is close to the city of Aleppo and its international airport.
However, Iran's Tasnim news agency cited the commander of an Iranian-backed Afghan militia as denying that its base near Aleppo was struck.
The SOHR cited its sources as saying 26 pro-government fighters were killed in the strikes. Four were Syrian and the others foreigners, a vast majority of whom were Iranians, it said.
It also noted that the death toll might rise as 60 fighters were wounded, some of them seriously, and several others were missing.
The SOHR said that given the nature of the targets, the attacks were likely to have been carried out by Israel.
But Israeli Intelligence Minister Yisrael Katz said on Monday morning that he was "not aware" of the strikes.
"All the violence and instability in Syria is the result of Iran's attempts to establish a military presence there. Israel will not allow the opening of a northern front in Syria," he told Israel's Army Radio.
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