According to Reuters, the incident took place on the morning of September 8 (local time) at the Allenby Bridge border crossing controlled by Israel.
The Israeli military said a man driving a truck from Jordan drove straight to the Allenby Bridge border crossing. He jumped out and began shooting at areas where Israeli security forces were operating.
The gunman was killed shortly afterwards, but his identity was not revealed.
Although the shooting did not cause any serious damage to Israeli military forces, it took the lives of three nearby residents.
Israel's Magen David Adom (MDA) rescue force was immediately dispatched to provide first aid to the victims.
Medical professionals attempted to resuscitate the three victims but were unable to save their lives due to the severity of their injuries. MDA later declared the three victims dead.
The motive for the crime is still unknown and Israel is investigating further.
The Israel Airports Authority has closed border crossings with Jordan, including Allenby Bridge, to facilitate the investigation.
Dozens of Jordanian truck drivers near the scene of the shooting were questioned by Israeli forces. Israel also ordered the drivers to unload their cargo for inspection.
While Israeli and Jordanian authorities are urgently investigating this serious incident to protect the relationship between the two countries, Hamas is praising the gunman's actions.
Hamas official Sami Abu Zhuri said this was a protest against Israel's attack on Gaza and expected more similar incidents.