The threat, from a group calling itself The Group of Death, was made in a video obtained by Associated Press Television News.
"We will cut the road between Jordan and Iraq so that Jordanian supplies cannot supply the US Army," the speaker on the tape said, adding that it would happen in 72 hours from 1pm on Tuesday.
The video showed seven masked men dressed in black with rocket-propelled grenade launchers and rifles.
The group's warning comes amid a wave of captive-taking, most of the victims being truck drivers who entered Iraq from neighbouring countries to deliver supplies and other cargo.
A fighter who read a statement on the tape criticised Jordan, as well as Kuwait, for letting transportation companies enter Iraq to support the US-led occupation.
"We consider all Jordanian interests, companies and businessmen and citizens as much a target as the Americans," the speaker said, adding that trucks carrying medicine and food supplies will not be attacked.
"We have warned you so there will be no excuses," the group said in the statement, referring to the support provided by Jordan's King Abdullah II, a close US ally, to US and South Korean forces in Iraq.
King Abdullah (R) recently met
with Iraqi premier Iyad Allawi
"Jordan is forgetting the sacrifices of the (Iraqi) martyrs ... (and the) mujahedeen, who have sworn by God to get rid of the occupiers who began with Iraq and will continue with other Arab countries," the speaker said.
Relatives of two Jordanian drivers captured in Iraq threatened on Tuesday to behead the director of the company and kill all of its employees if he does not immediately comply with the captors demands and cease operations in Iraq.
Fayez Saad al-Udwan and Ahmed Salama Hassan - who work as drivers for the private Jordanian company Daoud and Partners - were kidnapped on Monday by a group calling itself the Mujahedeen Corps in Iraq.
The group warned they would be killed within 72 hours unless their employer withdrew from Iraq and stopped cooperating with US-led forces there.
The company provides construction and catering services to the US military in Iraq.