The incident, in the village of Majdal Shams, occurred on the day Palestinians held demonstrations to mark the "Nakba" or catastrophe of Israel's founding in 1948.
Dolan Abu Salah, the village's mayor, said between 40 and 50 Nakba demonstrators reached Majdal Shams, on the Israeli side of the frontier of the normally quiet Golan Heights.
"The way it was reported to me, they broke through the fence," he told the radio, which reported that dozens of people were wounded by gunfire.
The Israeli military declined immediate comment.
Israel captured the Golan Heights, a strategic northern plateau overlooking the Sea of Galilee, from Syria in a 1967 war.
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