He spoke hours after Israeli troops and Syrian forces exchanged fire across the sensitive ceasefire line on the Golan Heights, but the Jewish state denied Syrian claims one of its vehicles had been destroyed.
The Syrian army "fired on an Israeli patrol, which we confirmed six hours ago, but did not destroy a vehicle or kill anyone," Israeli military spokesman Avichai Adraee wrote on Twitter.
"In response, Israel Defence Forces returned precise fire at the source of the gunfire. They reported a direct hit," an army statement added.
Syria claimed to have destroyed an Israeli military vehicle it said had crossed the ceasefire line during the incident.
"The vehicle passed the ceasefire line and was moving towards the village of Bir-Ajam situated in the liberated Syrian zone" of the Golan, it said, adding that the operation was aimed at "lifting the morale" of rebel forces in the region.
Gantz said that the vehicle never entered Syrian-controlled territory and suggested that Syria was fabricating a story with an obsolete Israeli vehicle left behind in Lebanon during Israel's 2006 war there against Syrian ally Hezbollah.
"It's a totally absurd story about an old 2002 model jeep," he said.
On Monday too, the army reported that small-arms fire from Syria hit the Israeli-occupied Golan overnight, causing no casualties or damage. The army filed a complaint with the UN monitoring force.
The strategic plateau has been tense since the beginning of the conflict in Syria more than two years ago.
However, there have been only minor flare-ups in the area to date, with Syrian shells crashing in the occupied Golan and Israel firing in retaliation.
In recent weeks, there were four incidents of fire coming from the Syrian side of the ceasefire line.
Last week projectiles from Syria hit Mount Hermon, causing the popular site on the Golan to close down to visitors.
Defence Minister Moshe Yaalon said that Israel did not want to get sucked into Syria's war, but that fire on Israeli targets would not be tolerated.
"Our policy is clear: we will not intervene in the Syrian civil war, but concerning the situation in the Golan Heights, we will not permit gunfire against our territory," he said in a statement.
Maariv daily quoted an Israeli commander in the north of the country as warning that "if one of these shells causes an (Israeli) casualty, the response will be different."
Israel launched air raids inside Syria this month targeting what sources said were arms destined for its arch foe Hezbollah, whose members have joined the fight against rebels alongside the Syrian military.
The strikes ramped up regional tension, with Syria threatening to hit back.
In a separate incident on Tuesday, the Israeli army said an injured Syrian was taken to a hospital in northern Israel overnight after crossing the ceasefire line.
A number of wounded Syrians have been treated in Israeli hospitals over the past few months, before being repatriated.
Israel, which is technically at war with Syria, seized 1,200 square kilometres (460 square miles) of the Golan from its Arab neighbour in the 1967 Six-Day War.
It annexed the territory in 1981 in a move never recognised by the international community.
The area is thickly-sown with landmines and the Israeli army said that one of its sappers was killed on Tuesday during clearance operations in an Israeli minefield in the southern Golan.
Public radio said that the man stepped on an anti-tank mine which should not have exploded under the weight of a person.