A Syrian military source cited by state television in Damascus said, however, that the vehicles that were struck on Wednesday did not belong to Syria's armed forces.
Damascus has accused Amman of backing the three-year insurgency against President Bashar al-Assad by training and arming militants, but Jordan denies this and says it has tightened its border and jailed dozens trying to cross it illegally.
Wednesday's air strikes were the first time Jordan has used fighter jets to deal with such infiltrations.
"Royal air force fighter jets today at 10:30 am (0730 GMT) destroyed a number of vehicles that attempted to cross into Jordan from Syria," the Jordanian army said in a statement.
"The camouflaged vehicles tried to enter from an area with rugged terrain.
"The fighter jets fired warning shots, but they were ignored, prompting them to destroy the vehicles. The army will not tolerate such actions," said the statement.
A military official told AFP in Amman that "they were three wheeled vehicles which tried to enter the kingdom" near Ruwaished, in northern Jordan.
In Damascus, however, state television cited a military source as saying that the vehicles did not belong to the Syrian army.
"No military or armored vehicles belonging to the Syrian army moved towards the Jordanian border, and so what was targeted by the Jordanian air force does not belong to the Syrian army," it said in a breaking news alert.
Jordan's border guards have said they clashed with and arrested several people in recent weeks as they attempted to cross from Syria into the kingdom.
The kingdom has struggled to cope with hosting more than 500,000 Syrian refugees uprooted by the conflict.
At the same time, Amman says arms smuggling across the border with Syria has risen by 300 percent in the past year.
More than 150,000 people have been killed in Syria since the conflict broke out in March 2011, according to the Syrian Observatory for Human Rights, a Britain-based monitor.
HH/HH