Israel said the first strike was in response to earlier rocket fire.
Hours later, Israeli forces struck Aleppo airport in the north, the Syrian defence ministry said as regional tensions simmer over the Israel-Hamas war in Gaza.
The Syrian Observatory for Human Rights, a Britain-based monitor with a wide network of sources on the ground in the war-ravaged country, put the number of dead soldiers at 11, including four officers.
The strikes "destroyed arms depots and a Syrian air defence radar" and also targeted an infantry unit, it said.
Israel's army said its "fighter jets struck military infrastructure and mortars belonging to the Syrian army in response to the launches towards Israel" on Tuesday.
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