The gunfire erupted on Sunday at a residential building where the embassy is located, injuring an Israeli guard. Reasons for the gunfire remain unclear.
One man, also Jordanian, also died of gunshot wounds.
Preliminary investigations indicated that the two Jordanian citizens had entered the residential building to do carpentry, a statement by Jordan's public security directorate said on Sunday.
However, the report by Petra said the second man is a doctor who owns apartments in the building.
The incident comes amid tensions in the Muslim world over restrictions on worship imposed by Israel at a holy site in Jerusalem.
On Friday, Jordanians held massive rallies in Amman and other parts of the country, protesting against Israel's increased security measures at Al-Aqsa mosque in Jerusalem, Islam's third holiest site.
In 1994, Jordan became the second Arab country after Egypt to establish diplomatic ties with Israel.
AFP adds: An Israeli security guard shot dead a Jordanian who attacked him with a screwdriver at the Israeli embassy compound in Amman, while a second Jordanian was accidentally killed, officials and a security source said.
The Jordanian had come to an apartment in an annexe building at the Israeli embassy, to install furniture and stabbed the security guard in the back with the screwdriver, Israel's foreign ministry said.The guard then responded by shooting dead the Jordanian worker, while the apartment owner who was there at the time was wounded and later died from his injuries, according to the foreign ministry and a security source.
The security guard was lightly wounded, the foreign ministry statement said.
The security source in Amman had confirmed earlier that two Jordanians were killed in a shooting in the area of the embassy.
"The first Jordanian, 17-year-old Mohammed Jawawdeh, succumbed to his injuries at the scene. The second, Bashar Hamarneh, a doctor who was in the residential quarter of the embassy at the time of the incident... died of his injuries after midnight in hospital," the security source said.
The injured Israeli is "deputy director of security at the Israeli embassy and is still receiving treatment in hospital", the source added.
Jordanian police said in a statement they were "informed late evening (Sunday) of a shooting at a residential building inside the compound of the Israeli embassy".
Police deployed to the scene and surrounded the area, the statement said, adding that the two Jordanians had gone into the building to carry out "carpentry work".
An investigation into the shooting was still underway, the police said.
Jordanian security forces deployed in the streets around the embassy when the incident occurred.
