The suspect was shot after he refused to remove his coat and began mumbling "Allahu Akbar."
It was not immediately known who was behind the incident, a police spokesperson said.
Signs at the vandalized site read "Deborah the prophetess" and coffins in the area were sprayed with blue graffiti.
The attack on Temple Israel was one of at least 14 acts of vandalism carried out against Jewish and minority-affiliated institutions.
The Kfar Saba cafe received an outpouring of support after a note with the Kach emblem was sent to the owners in response to their attendance at an anti-government protest.
The vandalism extends a pattern of attacks on Christian sites in Israel.
Two Jewish teenagers caused $100,000 in damages to graves in the Mount Zion cemetery.