A quarrel broke out between the two for unknown reasons, leaving the Jordanian with two gunshots in the shoulder and the Israeli stabbed in the chest.
The Jordanian died of his wounds while the Israeli remains hospitalized in critical condition, according to al-Ghad newspaper.
A security source told the newspaper that a cordon has been set up around the embassy.
Tension between Israelis and Palestinians has escalated over the weekend as Palestinians held mass protests against security measures around the al-Aqsa Mosque.
Three Palestinians were shot dead and 400 wounded in clashes so far. Palestinian President Mahmoud Abbas said he was cutting all ties to Israel after the deadly violence.
Earlier on Sunday, Jordan requested an urgent meeting for Arab foreign ministers to discuss the situation.
Israeli embassy in Amman.
One Jordanian died on Sunday after a fight with an Israeli took place inside the Israeli embassy in Amman, local media reported.
