A BBC reporter at the scene says the immediate vicinity has been locked down but authorities have not released details. Media reports citing security sources say one Jordanian was killed and one Israeli seriously injured.
It said two Jordanian men working for a furniture firm had entered the embassy before the shooting. The dead Jordanian was killed by a gunshot, while the two wounded people were taken to hospital, the statement said.
Israeli authorities are believed to be evacuating embassy staff. The heavily protected embassy is located in the Rabiyeh neighbourhood, an affluent part of Amman.
On Friday, thousands of Jordanians protested in Amman against Israel over the installation of metal detectors at a site sacred to both Muslims and Jews in Jerusalem.
Israeli authorities are not commenting on the incident and have imposed reporting restrictions.