Jorge Moreira da Silva, head of the UN Office for Project Services, declined to say who carried out the strike but said the explosive ordnance was "dropped or fired" and the blast was not accidental or related to de-mining activity.
He did not provide the nationalities of those killed and wounded.
The UN body, known as UNOPS, carries our infrastructure and development projects around the world.
The Israeli military, which has carried out a heavy wave of air strikes since early Tuesday, denied earlier reports that it had targeted the UN compound.
But Moreira da Silva said strikes had hit near the compound on Monday and struck it directly on Tuesday and again on Wednesday, when the staffer was killed.
He said the agency had contacted the Israeli military after the first strike and confirmed that it was aware of the facility's location.
"Israel knew this was a UN premise, that people were living, staying and working there," he said.
There have been no reports of rocket fire or other Palestinian militant attacks since Israel unleashed the air strikes overnight and into Tuesday, ending a ceasefire that took hold in January.
The Israeli bombardment continued into Wednesday, although at a lower intensity.
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