The closure is the latest disruption to hit the country's troubled economy in recent months, after militias seized a series of oil and gas terminals, severely cutting production and sapping much-needed state revenue.
The protesters blocked entrances to the offices of The Arabian Gulf Oil company, a branch of the state-owned National Oil Corporation, in the eastern port city of Tobruk, the official said. They also blocked a road intersection leading to the refinery and forced the administration to halt production of fuel and natural gas destined for local consumption, he added.
The official spoke on condition of anonymity because he was not authorized to speak to the press.
Since the summer, militias have closed Tobruk's main al-Hariga terminal and four other oil export terminals in the country's east, demanding semi-autonomous status for the region that produces the majority of Libya's oil.
Local militias this past week split into two factions, one of which struck an agreement with the government to reopen the terminals within a week. But with another faction unsatisfied, it is unclear whether the ports will remained blocked.
Libya's heavily armed militias, many made up of former rebels who fought against former dictator Moammar Gadhafi, have proliferated since the 2011 civil war that ended with the dictator's ouster and death.
Zidan himself was briefly kidnapped by a militia group that was on the government's own payroll.
With assassinations of public figures and security officials frequent, much of the lawlessness is blamed on the groups. But the government also relies on many of them to provide security in the absence of a functioning police force.
Since the militias began blocking oil production last summer, Libya's output has plummeted to only a few hundred thousand barrels per day, from a previous 1.4 billion barrels.
The government says the closure costs the state some $130 million a day.
Also Wednesday, a separate refinery in the western city of al-Zawiya, some 30 miles from Tripoli, reopened after protesters shut it down for a day, state news agency LANA said.
Former rebels wounded while fighting Gadhafi's forces had shut down the site, which LANA said provides the country with 23 percent of its fuel needs.