Thousands of people have demonstrated against Israel in Amman in the past two weeks, while the speaker of the Jordanian parliament praised those who carried out the attack on the Israeli policemen, even though Jordan's King Abdullah condemned the attack in a telephone conversation with Netanyahu.
Sunday's incident is among the most serious since Israel and Jordan signed a peace treaty in 1994, the BBC reported Monday.
Netanyahu welcomed the guard after his return to Israel and was seen in a photo embracing him.
The metal detectors had triggered widespread Muslim protests, amid allegations that Israel was trying to expand its control at the site under the guise of security - a claim it denied.
The Israeli was in an "unstable" condition, the news site said.
A senior cleric says Muslims should stay away from a major Jerusalem shrine, pending a review of the new Israeli security arrangements there.
The incident took place at a privately-owned building rented by the Israeli government as a residence for some of its consular employees.
Dr. Oded Eran, former Israeli ambassador to Jordan, said security measures at the embassy in Amman would be stepped up, but Jordan would also need to take steps.
"The security cabinet accepted the recommendation of all of the security bodies to incorporate security measures based on advanced technologies (smart checks) and other measures instead of metal detectors", Israel announced early on Tuesday.
Two Jordanians have been shot dead and an Israeli wounded in the heavily fortified Israeli embassy compound in Amman.
Jordanian police said after Sunday's shooting that they sealed off the embassy compound and deployed dozens of anti-terrorism gendarmie forces. It has always been a flashpoint of anti-Israeli protests at times of turmoil in the Palestinian territories.
Jordan has made clear that the country expects Israel to jail the security guard, known in the media only by his first name "Ziv", for killing 17-year-old carpenter Mohammad Jawawdeh, who allegedly attacked Ziv with a screwdriver while delivering furniture to the embassy.
The Jordanian government then held the Israeli embassy staff hostage, and wouldn't let them leave the building or Jordan until Prime Minister Netanyahu agreed to the king of Jordan's demands, which Netanyahu apparently met, as the staff were finally freed on Monday night and rushed back to Israel.