The three men were among a group of smugglers that were spotted by “advanced observation” units on the border in the north-east of the kingdom, a military official said.
“Rapid response patrols were dispatched and the rules of engagement were applied by hitting them with direct fire,” the official said,
He said that 233,000 Captagon pills were found with the dead men, whose nationalities were not disclosed.
Captagon constitutes the core of drug smuggling from areas in southern Syria under government control into Jordan. Much of the Captagon is then smuggled out of the kingdom into the Arabian Peninsula.
The last time smugglers from Syria were believed to have been killed by Jordanian border forces was in November last year, when activists in the southern Syrian province in Suwaida said that the bodies of four smugglers had been found near the border.
Jordanian security forces closely monitor the northern part of the country to curb the trade in Captagon and other drugs, which are manufactured mainly in Syria and Lebanon.
Official television said on Sunday that security forces had discovered another 10,000 Captagon pills and 1kg of crystal methamphetamine hidden in a trailer that had arrived from Syria at Nassib, the only open border crossing between the two countries.
The border with Syria has become the main conduit for the trade since Syrian government forces retook the area from rebels in 2018 after a deal between Russia, the US and Israel.
Jordan says pro-Iranian militias in southern Syria and the Syrian military are behind the rise in drug smuggling over the past four years.
The 2018 agreement was supposed to keep Lebanon's Hezbollah and other Iran-backed groups away from the border.