According to police reports, two Jordanians worked for a furniture firm and entered the embassy compound before the shooting to do repairs. Police did not identify the wounded Israeli, and few other details were immediately available, Reuters reports.
Israel has imposed a ban on reporting the incident and has made no public comment.
The fortress-like embassy in the affluent Rabae district of the capital Amman is protected by Jordanian gendarme. It has long been a flashpoint of anti-Israeli protests at times of turmoil in the Palestinian territories.
Read alsoThree Palestinians shot dead after killing Israeli officer – mediaViolence against Israelis is rare in Jordan, a tightly policed country that is also a staunch regional ally of the United States and signed a peace treaty with Israel, the Arab neighbor with which it shares a long border.
But tensions have escalated between the two countries since Israel installed metal detectors at entry points to Al-Aqsa mosque in Jerusalem after two Israeli policemen were shot dead by three Arab-Israeli gunmen on Friday near the site.
The new security measures have triggered the bloodiest spate of Israeli-Palestinian violence for years.
Jordan has called for the removal of the metal detectors and thousands of Jordanians have protested against the Israeli move in an outpouring of public anger against Israel.
Jordanian police said after Sunday's shooting that they sealed off the embassy compound and deployed dozens of anti-terrorism gendarme forces.
"We have started a large scale investigation into the incident and ordered the prosecutor general to look at all the details," the police said in a statement.
Read alsoOver 500 Russian mercenaries, who earlier fought in Donbas, now taking part in Syria warIsrael 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.
King Abdullah's Hashemite monarchy has been custodian of the sites since 1924, paying for their upkeep and deriving part of its legitimacy from the role.