"You are killing Palestinians, we will hijack your servers," read a message on the home page of the targeted sites on Wednesday morning.
Hapoalim, the largest bank in Israel, was attacked, as well as Rambam hospital in the northern city of Haifa, Israeli media said.
The Jerusalem post newspaper said the attacks were the work of a hacking group called Team Evil, purportedly based in Morocco.
The group had claimed responsibility for attacks on US government websites in 2004, the newspaper said.
Pro-Palestinian hackers have launched a series of attacks on Israeli and pro-Israel websites in the past - particularly around the start of the second Palestinian intifada in 2000.
Israeli troops entered Gaza on Sunday to secure the release of an Israeli soldier captured by Palestinian resistance fighters on Sunday.