Information Minister Sameeh Maaytah said Bilal El-Labloubi died instantly of a bullet wound in his neck, the Associated Press reported.
A border official said two people managed to sneak in, while about 10 others ran back into Syria under heavy Syrian gunfire. It was not immediately clear if the two were the boy's parents. Maaytah said there was no cross-border fire.
He said the early Friday incident took place in Turra, a northern town near Ramtha on the Syrian border. Jordan hosts more than 140,000 Syrian refugees.
Meanwhile, the United States said it fears the Bashar al-Assad regime is preparing to carry out a massacre in the country's most-populous city, Aleppo.
State Department spokeswoman Victoria Nuland said the deployment of tanks, helicopter gunships and fixed-winged aircraft suggested such an attack, a "serious escalation," was imminent, the BBC reported.
Syrian rebels in Aleppo have begun stockpiling ammunition and medical supplies in preparation.
Nuland said: "Our hearts are with the people of Aleppo. And again, this is another desperate attempt by a regime that is going down to try to maintain control."
But she insisted that the U.S. would not intervene other than by providing non-lethal assistance to the rebels.