Relations had been cemented in a peace deal in 1994 but reached crisis point three years later when Mossad intelligence officers tried but failed to assassinate senior Hamas official Khaled Meshaal in Jordan.
The incident happens on the background of the Jerusalem Temple Mount terrorist attack and the following massive manifestations against Israel in the West Bank, Gaza and some Arab world countries, including Jordan.
Israeli media said Jordan has demanded to conduct an investigation and has prevented Israeli embassy staff from leaving the premises.
Muslims call the site Haram al-Sharif, while Jews consider it to be the holy Temple Mount.
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"We are holding contacts with Jordanian security and government officials in order to bring the incident to a close ASAP", he said in a statement.
The Israeli guard was lightly hurt, the media reports said.
According to a Foreign Ministry statement, the guard shot the assailant - identified as Mohammed Zakaria al-Jawawdeh, 17 - in self defense.
Oded Eran, a former Israeli Ambassador to Jordan, noted to NBC News that while there's been good cooperation between Israel and Jordan behind the scenes, the "unnecessary noise coming from the Jordanian government" on a public level isn't helping ease tensions.
Police earlier said one person had died and two were injured in the incident in the residential Rabiyeh neighbourhood of Amman.The injured Israeli is "deputy director of security at the Israeli embassy and is still receiving treatment in hospital", the source added.
Security cameras have now also been installed at a gateway leading to the site.
The embassy has been a meeting point for protests regarding turmoil in the Palestinian territories. They or their parents or grandparents were expelled or fled to Jordan in the fighting that accompanied the creation of Israel in 1948.