Soldiers shot the man in the knee after spotting him trying to cut through the border fence and first firing warning shots into the air, military spokeswoman Lt. Col Avital Leibovich said. A group of Syrians evacuated him, she added.
"Lately, we have had quite a few cases of people approaching the fence," Leibovich said. "We will not allow any breaching of the border into Israel."
Tens of thousands of Syrians have fled their country since the revolt against President Bashar Assad began 17 months ago, mostly to Jordan and Turkey. Heavy fighting begun last month has hastened the flow, and the United Nations estimates as many as 1.5 million could be displaced inside the country with little or no access to aid.
Asked by a reporter if the man was a refugee fleeing the escalating violence in Syria, Leibovich said the military does not consider him as such. She said Israel's political leaders are the ones responsible for deciding whether or not to treat attempted Syrian infiltrators as refugees.
The other men who tried to enter the Golan were disguised as shepherds, she added.
Israel's military says it has observed a spike in the number of Syrians attempting to cross into the Golan in recent weeks.