The bus was hit in the Anjara area west of Aleppo at 9:30 am (0630 GMT), SANA said. Militants attacked the vehicle with an anti-tank rocket, it added, giving no further details.
The Syrian Observatory for Human Rights said opposition fighters carried out the attack and that the death toll would likely rise.
There was no immediate claim of responsibility.
Syrian rebel group Ahrar al-Sham posted a video on its Telegram channel on Friday showing a rocket hitting a bus, with a caption saying it showed the moment a military bus belonging to pro-Assad militias was destroyed west of Aleppo.
Reuters could not independently verify the reports or the video.
Hours after the attack, Russian warplanes carried out air strikes on rebel-held areas in the northwest, the Observatory reported, saying it had no immediate information on the results of the air strikes.
The men killed in the attack west of Aleppo were pro-government Shi'ite fighters from the towns of Nubl and Zahraa, said a pro-Damascus military source and the Observatory, which reports on the war using what it describes as a network of sources on all sides of the war.
The government has relied on local paramilitary forces and allied fighters from countries including Lebanon and Iraq to take back swathes of territory in the 11-year war.
The head of Lebanon's heavily armed Shi'ite movement Hezbollah, which has intervened in Syria in support of President Bashar al-Assad, announced his condolences later on Friday in a televised address.
Northwestern Syria is the last major stronghold of insurgents fighting the government and its allies. Turkish forces, which back some rebel groups, are deployed in the rebel-held area.
The main frontlines in the conflict, which spiralled out of protests against Assad in 2011, have been largely frozen for several years. Russia deployed its air force to Syria in 2015 in support of the Syrian government.