The book, "No Easy Day," is the unauthorized blow-by-blow telling of the daring raid on bin Laden's Abottabad compound in Pakistan last May.
Drafted by the Pentagon's intelligence directorate, the rules say DOD employees can buy copies of the book, which would not be treated as classified information.
But employees “shall not discuss potentially classified and sensitive unclassified information" contained in the book with family, friends or other individuals "who do not have an official need to know and an appropriate security clearance," the new rules state.
Those cleared DOD employees with detailed knowledge of the raid or access to that information “shall not publicly speculate or discuss potentially classified or sensitive unclassified information outside official U.S. Government channels," according to the new rules.
All employees “are prohibited from using unclassified government computer systems to discuss potentially classified or sensitive contents" of the book, according to the Pentagon.
Department officials are also banned from engaging "in online discussions via social networking or media sites" about sensitive information that may or may not be included in the book, according to DOD.
The Washington Times first reported details of the new rules on Wednesday.
The book's author, a former member of the Navy's vaunted SEAL Team Six, was a member of the American assault team that led the Abottabad raid, which ended in the death of the infamous al Qaeda leader.
Since its release, the book and its author — who penned the best seller under the pseudonym "Mark Owen" — have drawn sharp rebukes from Pentagon officials and the White House over its telling of the mission, code-named Operation Neptune Spear.
DOD officials have threatened legal action against Owen, alleging he broke the non-disclosure agreement he signed while still with the SEAL teams by including sensitive and classified details of the mission in the book.
Special Operations Command chief Adm. William McRaven sent a command-wide notice warning other U.S. special-operations forces members against following in Owen's footsteps, shortly after the book went public.
Command officials would pursue "every option available" to punish other U.S. special operators who break the non-disclosure pact, McRaven said in the notice.
The four-star admiral also met with other SEAL Team Six members who participated in the Abottabad mission, to confirm the details about the operation Owen included in the book.