State TV reported several missiles hit the Kfar Sousseh area, in the western part of the city, on Wednesday morning.
The pro-government Sham FM radio station said the alleged strike hit a building near an Iranian school and caused casualties.
Rami Abdurrahman, who heads the Syrian Observatory for Human Rights, a Britain-based opposition war monitor, said the two killed were inside an apartment but did not give any clues about their identities.
He added that the strike was similar to last month's killing in Beirut of Saleh Arouri, a top official with the militant Palestinian Hamas group.
Israel has not yet commented on the alleged strike.
The strike damaged the fourth floor of a 10-story building, shattered window glass on nearby buildings and also damaged dozens of cars parked in the area. An empty parked bus for the nearby Al-Bawader Private School was also damaged and people were seen rushing to the school to take their children.
Israel has carried out hundreds of attacks on targets inside government-controlled parts of war-torn Syria in recent years.
Israel rarely acknowledges its actions in Syria, but it has previously said it targets bases of Iran-allied militant groups, such as Lebanon's Hezbollah, which has sent thousands of fighters to support Syrian President Bashar Assad's forces.
In January an Israeli strike on the area of Mazzeh, also in Damascus, destroyed a building used by the Iranian paramilitary Revolutionary Guard, killing at least five Iranians.
In December, an Israeli airstrike on a Damascus suburb killed Iranian general Seyed Razi Mousavi, a long-time adviser of the Iranian paramilitary Revolutionary Guard in Syria.
Israel has also targeted Palestinian and Lebanese operatives in Syria over the past years.
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