"The situation in Ras Lanouf is catastrophic for the enviroment," it said in a statement.
State news agency LANA reported that IS militants were behind the attack and that the storage tankers belonged to Harouge Oil Operations.
Nobody has claimed responsibility for the attack, but Mohamad al-Manfi, the spokesman for NOC in the east, said the jihadists had "fired rockets at the oil tanks".
"Five tanks belonging to the Harouge company are still on fire. Firefighters are at the site trying to extinguish the blaze," Manfi told AFP late Thursday.
"But we don't have sufficient means to put out the fire," he added, describing the situation as a "disaster".
The company has 13 storage tankers with a combined capacity of 6.5 million barrels at its site about nine kilometres (six miles) from the port of Ras Lanouf.
- 'Destroying Libya's future' -
IS, a growing power in strife-torn Libya, has in recent weeks launched repeated attacks from its base in the city of Sirte on facilities in the "oil crescent" along Libya's northern coast.
Libya sits on estimated oil reserves of 48 billion barrels, the largest in Africa, but production has plummeted since the country descended into chaos following the 2011 ouster of Moamer Kadhafi.
Analysts have warned that IS seizures of major oil facilities would be a crippling blow to Libyan authorities and a major boost for the jihadist group.
Western governments have expressed fears over the attacks.
"Another attack on #Libya's oil installations in Ras Lanuf. #Daesh are destroying Libya's future economic recovery," Britain's ambassador, Peter Millett, said on Twitter, using an Arabic acronym for IS.
Foreign powers have been pushing for a long-delayed political deal to resolve the political paralysis in Libya that has allowed IS to thrive.
A national unity government was formed on Tuesday under a UN-brokered deal aimed at ending political divisions that have seen the country torn between rival administrations and parliaments.
But it was unclear how much support the new government commands, especially among Libya's myriad armed groups, and whether it would be able to exert any authority.
The UN envoy to Libya, Martin Kobler, on Thursday renewed an appeal for the country's political forces to stand together.
"Once again Libya's resources under terrorist attack in Ras Lanouf. Political process must urgently catch up (with) military developments," he wrote on Twitter.
- 'Perfect chaos' -
The unity government, headed by Fayez al-Sarraj, has not yet been approved by either of the country's rival parliaments.
Libya's internationally recognised government and parliament are operating out of the country's east after being forced out of Tripoli by a rival administration in mid-2014.
Efforts to form a fully functioning government have been given added urgency by fears IS is building a new stronghold in Libya, just across the Mediterranean from Europe.
The jihadist group has carried out a wave of attacks in Libya, including a suicide truck bombing on a police school in the city of Zliten earlier this month that killed dozens.
As in areas under its control in Syria and Iraq, the group has committed atrocities in Libya, including execution-style murders of its opponents.
Photographs posted online by the group in Sirte on Thursday showed the executions of four men shot in a public square for theft, blasphemy, heresy and belonging to forces loyal to the recognised government.
Meanwhile, the EU's counter-terrorism coordinator said IS's military losses in Syria and Iraq may prompt some of its leaders to relocate to Libya where they will face less pressure.
"There, for the time being, it's the perfect chaos they like," Gilles de Kerchove told AFP, in reference to Libya.