The armed man, who came from a Palestinian refugee camp in Syria, on Friday penetrated a border fence.
He fired nine rounds into an Israeli army post in an attempt to explode a petrol container, the AFP news agency said, quoting Israeli officials.
Speaking to Aljazeera, spokesperson for the Israeli army Major Etan Arusi said, "We have learned that he is a Syrian of Palestinian origin as he was holding a Syrian ID card."
During questioning, the armed man said he was a member of one of the Palestinian factions, which might be Fatah, the Palestinian ruling faction. But this information has not yet been verified, Arusi said.
The man dug a trench under a fence on the Syrian-Israeli border and penetrated Israel to carry out attacks against Israeli forces in Golan Heights, Arusi said.
When asked whether it was an individual or an organised operation, Arusi said, "What I can say is that the person is still under investigation".
AFP quoting a military source said the attacker intended to abduct a soldier and take him back to Syria.
Peace talks' failure
Israeli and Syrian negotiators last held peace talks in 2000 that foundered over the future of the Golan Heights, occupied by Israel since the 1967 Middle East war.
Syria has called repeatedly for the talks to resume.
Israeli Prime Minister Ariel Sharon has said Syrian forces must first pull out of Lebanon and stop supporting Lebanese guerrillas and Palestinian fighters before Israel would consider negotiations.