The senior official compared the cyberattack to a "terrorist operation," The Financial Times reported.
Deputy Foreign Minister Danny Ayalon said the attack represented "a breach of sovereignty comparable to a terrorist operation, and must be treated as such. Israel has active capabilities for striking at those who are trying to harm it, and no agency or hacker will be immune from retaliatory action," the Times reported.
Last week, a Saudi-based hacker -- "0xOmar" -- posted credit card details affecting at least 14,000 Israeli cardholders, and claimed to have access to a far greater trove of personal data.
The hacker claimed he had uncovered the credit card details of about 400,000 Israelis, but later said he had personal information on 1.1 million Israelis, the Times said.
Israeli media said there has been little financial damage so far due to the cyberattack.
The Israeli daily Yedioth Ahronoth published what it said was an e-mail exchange with 0xOmar Friday. In the exchange, the hacker said the cyberattack was politically motivated and added, "I want to harm Israel financially and socially."