One of the Jordanians was critically wounded and later died at a hospital, according to Hala Akhbar, a news site linked to the Jordanian military.
At least one person is dead in a shooting incident at the Israeli embassy in the Jordanian capital Amman, a Jordanian security source says.
It said two Jordanian men working for a furniture firm had entered the embassy before the shooting.
The heavily protected embassy is located in the Rabiyeh neighbourhood, an affluent part of Amman.
Israel's foreign ministry had no immediate comment.
The incident comes amid mounting tensions between Israelis and Palestinians over metal detectors that Israel has installed at a contested shrine in Jerusalem.
Israel has in the past given repeated assurances that it understands Jordan's concerns and does not seek to alter the status quo in the Muslim holy sites of Jerusalem.
In Jordan, thousands demonstrated Friday in an effort to spark further protests in Amman and in refugee camps across the kingdom.
Many of Jordan's 7 million people are of Palestinian origin.
Israel's said its decision to enhance security came after two border police officers were killed in an attack at the compound a week ago. The attackers fled into the compound and were shot dead by Israeli security forces.
The country's officials have said they are open to adopting alternative security measures in order to reduce tensions, but have warned they will not remove the metal detectors.