Millions in Somalia and across the Horn of Africa face dire food shortages in the worst regional drought for decades.
The Islamist al-Shabab militia, which controls much of Somalia, has banned the WFP from its areas.
The delivery was to have begun on Tuesday but was delayed from leaving Kenya by bureaucratic hurdles.
Challiss McDonough, a spokeswoman for the WFP, said the 10 tonnes of Plumpy'nut, a peanut-based paste high in protein and energy, would be enough to treat 3,500 malnourished children for one month.
Given the demand for food aid in Somalia, the delivery is just a drop in the ocean, says the BBC's East Africa correspondent Will Ross, in Nairobi, Kenya.
The Plumpy'nut was flown from France to Kenya on Monday.
More flights were planned for the coming weeks, Associated Press news agency quoted Ms McDonough as saying.
Fleeing to Mogadishu The delivery is the first airlift of food aid since the UN declared a famine in two southern areas of Somalia last week.
Agencies banned by al-Shabab
- International Medical Corps
Tens of thousands of Somalis have fled areas controlled by al-Shabab to Mogadishu and neighbouring Kenya and Ethiopia in search of assistance. The weak interim Somali government, backed by an African Union (AU) force, controls only parts of Mogadishu.
A spokesman for the AU force, Lt Col Paddy Ankunda, told the BBC the Boeing 737 delivering the 10 tonnes of supplies had landed at Mogadishu's airport.
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More than 10 million people in the region are thought to be at risk.
Somali Foreign Minister Mohamed Ibrahim has warned that more than 3.5 million people "may starve to death" in his country.
The Prime Minister, Abdiweli Mohamed Ali, has complained that the UN is being too slow with the delivery of food.
The challenge facing all aid agencies is immense but some analysts are questioning why this emergency was not prevented - as the severe drought and food shortage were predicted late last year, says our East Africa correspondent.
After criticisms that wealthy Arab states were not doing enough to help with the crisis, Saudi Arabia has pledged $50m (£30m) to the WFP to buy food for Somalis, the UN agency has said.
It follows an announcement from the European Union that it would donate $40m on top of the $61m it had already given the drought-hit region of East Africa this year.