The same area was heavily damaged in the ammonium nitrate explosion that leveled the central port area and the adjacent waterfront on August 4.
According to Lebanon's civil defense agency, the fire has been substantially brought under control as of Thursday afternoon, if not yet entirely extinguished.
Newly-appointed port director Bassem Kaissi told Al Jazeera that the facility that caught fire was a warehouse leased to BCC Logistics.
The firm had reportedly been working on rebuilding the facility when the fire broke out, and its fire detection and suppression systems had not yet been restored.
The fire could have an effect on humanitarian relief operations related to Beirut's last port disaster, according to Fabrizio Carboni, the Mideast regional director for the Red Cross.
"The warehouse on fire is where [the Lebanese Red Cross] stocks thousands food parcels and 0.5 million liters of oil.
The extent of the damage still remains to be established.
Our humanitarian operation risks to be seriously disrupted," Carboni said in a statement.
ICRC confirmed that some portion of its stock of food parcels at the warehouse had caught fire, though the exact amount is not yet known.
Ever since the blast on August 4, ICRC has been working to move the food out of the damaged warehouse, and by the time of the fire it had already relocated about 19,000 parcels.
Lebanon's minister of justice, Marie Claude Najm, has called for a thorough investigation into the cause of the new fire.
However, the call was not enough for Lebanese member of parliament Rola Tabsh, who demanded an international - not local - inquiry into the recent disasters at Port of Beirut.
"Beirut has burned from the fires of [the government's] corruption and arrogance," wrote Tabsh in a social media message.
Turkish maritime news