"It is the first time that a soldier in the Israeli army has joined the Islamic State," the agency said in a statement.
It said that the man is a Muslim and had slipped into Syria via Turkey a year ago to join IS.
Shin Bet did not identify the man, but said he was from an Arab village in the northern Galilee region.
According to the agency, around 35 Israeli Arabs have joined IS.
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And a number of Israeli Arabs have died fighting with jihadist groups in Syria, which has been wracked by war for nearly five years, judicial sources say.
Last week, Israel charged five Arabs from the northern city of Nazareth with having ties with the jihadist group.
And last month it arrested six others on suspicion of planning to travel to Syria to join IS, after another Arab man crossed from the Israeli-occupied Golan Heights into neighbouring Syria on a hang glider.
Israeli Arabs are Palestinians and their descendants who remained after the creation of Israel in 1948 and account for more than 17 percent of the country's population.
Military service is compulsory in Israel, including for Arab Druze who belong to an offshoot of Shiite Islam. But other Arab Muslims and Christians can enlist voluntarily.