The hacking incident was first reported by Motherboard on Tuesday. One of the hackers, who goes by the name Cracka, reached out to the publication claiming to have broken into a series of accounts associated with Clapper, including his personal email account.
Clapper's home phone, a Verizon FiOS account, was also reportedly forwarded to the Free Palestine Movement.
The hacker made a name for himself alongside his group, Crackas With Attitude, last year when they broke into the CIA director's personal AOL email account.
Whistleblowing site WikiLeaks later began publishing the contents of the email account, which included Brennan's draft SF86, a sensitive document that is used to determine a prospective candidate's eligibility to later receive classified materials.
However, none of the documents posted by WikiLeaks are said to be classified.
The FBI warned last year that US police and officials were targets of hacktivist groups, and should in particular "be aware of their online presence and exposure."
The same hacker group later successfully broke into a series of law enforcement systems that allowed police to share information in real-time.