"Today, several shells fired from Syria landed in the central Golan heights, adjacent to the Israel-Syria border," he told AFP.
Israeli military "forces carried out a pinpoint strike, targeting the source of the shooting. A hit was confirmed."
The spokesman said at least three shells were confirmed to have hit Israel. He could not say whether the army considered the incidents cases of stray fire spilling over from the conflict in Syria.
Army radio reported the Israeli attack demolished a Syrian military position.
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The Golan has been tense since the beginning of the conflict in Syria more than two years ago, but so far there have only been minor flare-ups as Syrian small arms fire or mortar rounds hit the Israeli side, prompting an occasional Israeli response.
Israel, which is technically at war with Syria, seized 1,200 square kilometres of the strategic plateau during the 1967 Six-Day War, which it later annexed in a move never recognised by the international community.
Dozens of Syrians, including women and children, have been treated in hospitals in northern Israel since the beginning of the uprising in their country.