The two Jordanians were working for a furniture firm and entered the embassy before the shooting, police say.
Few details have been revealed and what sparked the shooting is unclear.
Security forces have sealed off the embassy with the Israeli authorities evacuating staff.
The shooting happened in a residential building used by the Israeli embassy, Jordanian police say.
The three people were hospitalized, with one of the Jordanians dying from bullet wounds, according to a statement. It said investigations were still in their "initial phases".
