The guard's gunfire also apparently hit bystanders, Franco told Israel Radio.
The Ateret Cohanim yeshiva was founded in 1978 and is located in the heart of the Old City near the Temple Mount, the site revered by Jews that also houses the Al-Aqsa mosque, the third holiest site in Islam.
Israel occupied east Jerusalem in a war in June 1967 and quickly annexed it, declaring Jerusalem the "eternal and indivisble" capital of the Jewish state.
However, its claims are not recognised by the international community and Palestinians hope to make the eastern half of the city, where 200,000 Palestinians live, the capital of their promised state.
Ateret Cohanim is one of several ultra-nationalist organisations which have bought land and homes from Palestinians through various means in order to place Jews in the Arab neighbourhoods of east Jerusalem.