According to a Syrian military source, the missile attacks were carried out by Israeli Air Force.
It said that some civilian properties in the suburbs of Damascus suffered damage.
Israel does not usually comment on reports concerning its strikes in neighboring Syria, though it has recently acknowledged striking Iranian targets there.
The raids near Damascus and in Homs province late Sunday killed the fighters, but it was not immediately clear exactly how the civilians died - whether in the strikes or in the aftermath, the Syrian Observatory for Human Rights said.
In the Homs area, a research centre and a military airport where Iranian and Hezbollah personnel are based, were targeted, the Observatory said.
In Cyprus, the foreign minister said a Russian-made missile launched from Syria landed in its territory.
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The Syrian Observatory for Human rights, a United Kingdom based watchdog group, said Israel was targeting Iranian linked bases, including a base where Iran's Islamic Revolutionary Guard Corps forces are headquartered.
Near Damascus, a base hosting the Iranian Revolutionary Guards (IRGC) and a research facility in Jamraya were struck.
An Israeli military spokeswoman refused to confirm details about the attack.
Israeli jets and naval gunships targeted at least ten sites around Homs and Damascus, as well as the Syrian border with Lebanon, with Syrian air defense forces opening fire on Israeli missiles. It periodically attacks what it says are threats to Israeli security in Syria.
Iran and Hezbollah are sighting on the side of President Bash al-Assad in the Syrian war, and Israel said they are trying to turn Syria into a new front against the Israelis.