Prime Minister Benjamin Netanyahu has threatened to revoke the man's citizenship amid speculation he was trying to join a Syrian rebel group.
Witnesses reported intensive activity in the border area, including Israeli aircraft dropping illumination flares.
Israel officially maintains a neutral stance on the Syrian conflict.
Its citizens are banned from travelling there, but a small number of Israeli Arab citizens are understood to have gone to fight in Syria nonetheless - though few arrive by air.
It was believed that the man who flew into Syria on Saturday night was from Jaljulia, a mainly Muslim Arab town north-west of Tel Aviv, the military said.
The military said it had been unable to find the man despite intensive searches in the area where he landed near the Golan Heights - an area in south-western Syria annexed by Israel in 1981, in a move not recognised internationally.
Reuters news agency quoted a Syrian rebel whose group operates in the area as saying the paraglider had come down either in Syria's Quneitra province, which includes the Golan Heights, or in the neighbouring Deraa province.
Israel's Ynetnews reported he had been picked up by someone on the Syrian side after landing.
Israel's intelligence services are now said to be continuing the search.
A minister from Prime Minister Netanyahu's rightist Likud party, Ofir Akunis, is quoted as telling reporters that the Israeli Arab had "crossed to the border into Syria... to join ISIS [so-called Islamic State] forces".
"Whoever joins the enemy's ranks to fight Israel will not be an Israeli citizen," Mr Netanyahu said at the start of his regular Sunday cabinet meeting.
There were initial fears that he may have been blown into Syria by accident and could have been taken hostage.
But Israel Defense Forces (IDF) sources later said he had flown against the prevailing winds, suggesting the journey was undertaken deliberately.
"IDF surveillance post identified a paraglider entering Syria," the force said in a tweet. "Initial investigation suggests Israeli-Arab crossed intentionally."
Israel says one of its Israeli Arab citizens deliberately paraglided into Syria, amid reports of intensive Israeli aerial operations overnight.