Syrian state TV says that rockets have struck military positions in the countryside of Hama and Aleppo provinces.
A military source was quoted as saying by SANA that the "new aggression" by Syria's enemies had taken place at around 10:30pm (19:30 GMT) on Sunday.
The state TV outlet aired images of what it said was the explosions. It had earlier reported that successive blasts were heard in the Hama and Aleppo countryside and that authorities were investigating the cause.
SANA did not say who was responsible for the attacks.
Reporting from Aleppo, Al Jazeera's Maan al-Khoder called the strikes "one of the strongest attacks on the military".
"Civilians in Aleppo described hearing a huge explosion and their description is in line with what the state is saying," he said.
An official death tally was not yet given.
An intelligence source told Reuters news agency it appeared multiple missile attacks hit command centres for "Iranian-backed militias" fighting alongside forces loyal to Syrian President Bashar al-Assad.
Israel has previously targeted Iranian-backed militia outposts in Syria.
Andrew Tabler, a Syria expert at the Washington Institute for Near East Policy, said Israeli attacks targeting Iranian bases in Syria have continued for some time now.
"It seems as if it's an Israeli strike. It's yet to be confirmed but the targets in recent history of Israeli bombing inside of Syria would suggest that that's who's responsible," he told Al Jazeera.
"These are mixed bases for Iran and regime forces inside Syria, Iranian forces are spread out throughout the country.
"They are the main backers of Assad on the ground and Israel has launched a campaign to target those assets as they spread throughout the country."
Reporting from Beirut, Lebanon, Al Jazeera's Zeina Khodr said the fact that Syrian state media are not blaming anyone for the strikes sets it apart from previous attacks.
"This is quite different than in the past when there have been similar strikes, the Syrian government does not shy away from pointing the finger at Israel, which is believed to be behind these latest strikes," Khodr said.
Missiles struck a Syrian airbase in Homs earlier this month, with Russia and Syria blaming Israel for that attack. Israel neither confirmed nor denied that raid.
