“Rapid response patrols” attacked a group of smugglers as they crossed into Jordan from Syria on Saturday, he said.
It was the latest armed confrontation in Amman's drug war, taking place on the border with Syrian territory under the control of President Bashar Al Assad.
Some of the smugglers were wounded by “direct fire”, which prompted the others to flee to the Syrian interior, the spokesman said.
Jordanian officials have accused the Syrian military and pro-Iranian militias allied with it of overseeing the trafficking of narcotics, which they say are being increasingly consumed to Jordan as well as re-exported, mainly to Saudi Arabia.
Earlier this month Mr Al Assad denied his state was in any way involved with the drugs and blamed neighbouring countries he did not name for what he termed as “chaos” in Syria.
The Jordanian military spokesman did not reveal any details on the smugglers' identity or whether any were arrested. He said 63,000 pills of the amphetamine Captagon and 588 pouches of hashish were found at the scene.
On Wednesday, the Jordanian military announced the interception of a drone from Syria that was carrying TNT explosives.
The device differed from those which had previously been seized, which were generally small commercial drones carrying drugs.
In January 2020, the Jordanian military started reacting more swiftly and responding with more firepower to smugglers as the drug trade boomed and an illicit transit corridor developed through Jordan's territory into Saudi Arabia.
The US and other western backers of Amman also sent hundreds of millions of dollars to upgrade its border defences.
At the same time, Jordan embarked on a rapprochement with Mr Al Assad and supported the readmission of Syria to the Arab League in May.
Until then, Mr Al Assad had been largely ostracised for his violent suppression of the March 2011 revolt against his rule.