Israel fired back across to Syria in response. The Israelis responded, according to the military spokesman. A subsequent Israeli air strike destroyed a vehicle carrying four militants, Lerner said.
A military spokeswoman told EFE that the attacks were perpetrated by the Yarmouk Martyrs Brigade - an alleged IS-linked group fighting near the Israeli and Jordanian border.
"Our forces are prepared on our northern border, and we won't let IS elements or other hostile elements use the cover of the war in Syria to establish themselves next to our borders", he said in remarks relayed by his office.
Spillover from the civil war in Syrian has crossed into Israeli territory on a number of occasions, usually in the form of mortar and projectile fire, causing damage but no injuries.
At the same time, IDF soldiers reported hearing gunshots at the border.
Israel captured the Golan Heights from Syria in the 1967 Mideast War and the two countries remain enemies.
There is also considerable movement between different ISIS affiliates as the parent group changes priorities, so this could rapidly become a bigger force with an interest in going after Israel.
Israeli officials fear Hezbollah and Iran's al-Quds Force are aiming at using the area to open a new front against Israel in any future conflict. The militant group consists of some 700 operatives, Lerner said.
They came for salsa music and mojitos and ended up wandering through a city turned still and silent by nine days of national mourning for Fidel Castro.
An Israeli unit was conducting an operation beyond a fence that separates the Israeli-controlled Golan Heights and Syria but within the border when it was shot at by Islamic State militants, the army said.