In Tigray, a nearly two-year conflict has killed thousands of people and left millions in need of aid.
The drone strike on Sunday hit near an area called Zana Woreda in northwestern Tigray, the WFP spokesperson told Reuters.
"Flying debris from the strike injured a driver contracted by WFP and caused minor damage to a WFP fleet truck," the spokesperson said, adding it was not possible to say yet whether further distributions would be suspended in the area.
Two humanitarian workers, who asked not to be named, told Reuters that food distribution operations by another aid agency had been disrupted by shelling in Tigray.
Ethiopia's Government Communication Service said in a statement the government had asked aid organizations to avoid working in areas where it was taking preventive actions in response to attacks against it by the Tigray People's Liberation Front (TPLF), which governs Tigray.
The communication service said that in the past aid transport vehicles had been hijacked and that the TPLF had transported its combatants on trucks painted with U.N. logos.
The WFP truck was delivering food to internally displaced people, hundreds of thousands of which have been uprooted by renewed fighting since Aug. 24 when a five-month ceasefire ended, humanitarian sources say.
Since then, no truck carrying food aid has entered Tigray, the WFP said.
It says an estimated 13 million people in Tigray and neighboring regions of Amhara and Afar are in "desperate need of food assistance."
The conflict pits Prime Minister Abiy Ahmed's government against the TPLF, which used to dominate Ethiopia's ruling coalition.
The government accuses the TPLF of trying to reassert Tigrayan dominance over Ethiopia. The TPLF accuses Abiy of over-centralizing power and oppressing Tigrayans.