Shamai Kedem Leibowitz, 40, of Silver Spring, Maryland, who is the grandson of renowned Israeli philosopher Yeshayahu Leibowitz, was also sentenced to three years of supervised release by US District Court Judge Alexander Williams, the department said.
Leibowitz, also known as Samuel Shamai Leibowitz, pleaded guilty in December to one count of disclosing classified information to an unauthorized person.
Leibowitz acknowledged handing over five FBI documents concerning US communication intelligence activities to the blogger, who was not identified. The blogger then published information from the documents.
"The willful disclosure of classified information to those not entitled to receive it is a serious crime," assistant US attorney general for national security David Kris said in a statement.
"Today's sentence should serve as a warning to anyone in government who would consider compromising our nation's secrets," Kris said.
FBI special agent Richard McFeely said that as a "trusted member of the FBI ranks, Leibowitz abused the trust of the FBI and the American public by using his access to classified information for his own purposes".
Leibowitz was employed by the FBI from January to August 2009 as a contract linguist in an office in Calverton, Maryland. He held a "top secret" security clearance giving him access to classified documents.