The suspects have 10 days to comply with the order before the security forces arrest them, according to a court announcement on Thursday.
"If you don't hand yourselves within this period you will be considered fugitives," said Col Mouwafak Al Masaeed, the court president who signed the order.
Fugitive status means that the suspects' assets and holdings would be seized.
They have been charged with importing, exporting or marketing drugs.
The move came after the security forces carried out raids this week against narcotics networks across the kingdom, arresting 20 men in one day, police said.
Jordan's military-run state security court also deals with terrorism, political crimes and other threats deemed too grave or sensitive to be handled by the civil legal system.
Last week, as part of a toughened anti-narcotics policies, the authorities changed legal procedures to automatically try drug-linked money laundering cases in the state security court, instead of a civilian court.
Border operations have been stepped up in the past few months to disrupt flows of the stimulant known as Captagon and other drugs.
The drugs mainly come from areas controlled by the Syrian military and pro-Iranian militias, according to Jordanian officials. The Syrian government and Hezbollah deny any involvement in the drug trade.
The smuggling rose exponentially after southern Syria was captured by President Bashar Al Assad's forces in 2018 from rebels, who included units supported by the US, Jordan and other Arab countries.
The area is the birthplace of the 2011 revolt against five decades of Assad family rule. The uprising militarised by the end of the year after the regime responded with deadly force, sending tanks to crush demonstrations in the border city of Deraa.
The regime's takeover of the south occurred under a deal between Russia, the US and Israel.
Under this agreement, Hezbollah and other pro-Syrian regime militias would keep away from Syria's southern border, which connects Syria with Jordan and the occupied Golan Heights.