A statement by the Benghazi-based administration posted on X said it was "suspending all oil production and exports until further notice", citing "force majeure".
The locations affected constitute around 90 percent of the country's oil fields and terminals.
It linked the move to "repeated attacks on the leaders, employees and administrations of the Central Bank" based in Tripoli, which manages Libya's large oil resources and the state budget.
The eastern-based administration said "outlaw groups" were responsible for a bid to control "Libya's most important financial institution", the statement added.
Libya is struggling to recover from years of conflict after the 2011 NATO-backed uprising that overthrew longtime dictator Moamer Kadhafi.
It remains divided between the UN-recognised government in the capital Tripoli led by Prime Minister Abdulhamid Dbeibah, and the rival administration in the east backed by military strongman Khalifa Haftar.
Most of its oil fields are located in regions controlled by Haftar, but oil revenues as well as the state budget are managed by the Central Bank based in the capital, Tripoli.
'No effective power'
The eastern-based administration's decision to suspend operations came after a series of events which it said were attempts by the western-based government to seize control of the Central Bank.
The bank had said on August 18 it was "suspending all operations" after the abduction of its head of information technology.
The IT chief was released a day later and the central bank said it was resuming normal operations.
A week earlier, local media reported that armed men had besieged the bank to force the resignation of its governor, Seddik al-Kabir.
He has faced criticism from people close to Dbeibah over the management of oil resources and the state budget.
In its statement on Monday, the eastern-based administration said the "outlaw group" close to the Tripoli authorities had forcibly taken over the central bank.
Footage and photos broadcast by local media showed a group of people breaking into the bank's headquarters.
Reports later said members of a commission tasked by the presidential council, which is close to Dbeibah, with leading a "transition of powers", had installed a new board of the bank.
However, experts questioned whether the commission could run the bank effectively.
Anas El Gomati, head of the Sadeq Institute think tank, said their "holding the office doesn't mean controlling the purse strings".
Libya analyst Jalel Harchaoui told AFP the commission "has little real capacity to issue letters of credit, allocate salary budgets, and finance construction projects," among other things.
"Their physical presence does not give them any effective power over the Central Bank, which remains frozen following orders from Kabir," he said.
'Unilateral acts'
Harchaoui said "this does not mean that Dbeibah succeeded in his manoeuvre" to take control of the Central Bank.
Haftar's side had "established a new oil blockade in order to influence the situation in Tripoli and internationally".
"The possibility of a military offensive on its part on Tripoli cannot be excluded", he added.
On Friday, Tripoli-based Interior Minister Imad Trabelsi announced an agreement between armed groups and security forces in the capital to "secure" the city and its government institutions amid rising tensions.
Last week, the United Nations expressed concern about the rapid deterioration of the economic and security situation in Libya, denouncing "unilateral" moves by Libyan actors that have "increased tensions".
