SANA said people in the Golan Heights took to the streets in protest against what it called Israeli support for "the terrorist attack launched by Jabhat al-Nusra" on Hader. Nine people were killed and another 23 injured.
"In the aftermath of the terrorist attack, terrorist groups carried out a heavy attack on Hader, and army units and the Popular Defence units [pro-government militias] clashed with the attackers", Sans said.
Almost 140,000 members of the Druze minority, which follows a secretive offshoot of Shiite Islam, live in Israel and the Israeli-occupied Golan.
Al-Nusra Front is the old name for a jihadist group that was formerly Al-Qaeda's affiliate in Syria and is now known as the Fateh al-Sham Front.
Israel captured the Golan Heights from Syria in the 1967 Mideast War and the two countries remain enemies.
Opposed to the Syrian regime, the jihadist group is the dominant faction in the northwestern rebel-held province of Idlib.
The IDF said that it viewed the entry into Syria as a "serious security violation", and that soldiers had entered Syria in order to bring the Israeli Druze back.
Responding to some allegations by Druze that Israel was assisting Tahrir al-Sham, the Israeli military said "the allegations of Israeli involvement and assistance to global jihadi elements in the fighting are groundless".
Military spokesman Ronen Manelis said in a Facebook post that the army is "prepared and ready to assist residents of the village and prevent damage or occupation of the village out of a commitment to the Druze population".
An Israeli man from a Druze area in Israel was lightly wounded by stray fire from across the border amid "intense fighting" in Syria, earlier in the day, the military said.
Prime Minister Benjamin Netanyahu stated from London that Israel will continue to "guard our borders and to cherish our sympathy toward our Druze brothers".