Muse died shortly after arrival at a hospital in Merka, the UN source said.
Marcus Prior, a WFP spokesman, condemned the attack.
"WFP treats this incident seriously and we are shocked and saddened by the loss of one of our staff. This killing only underlines what a dangerous place Somalia is," he said.
In Mogadishu, witnesses said fighters loyal to the Islamic Courts Union (ICU) fired mortars at a base used by Ugandan peacekeepers serving under an African Union (AU) mandate.
Those at the base retaliated with artillery and small-arms fire, in an exchange that lasted several hours, witnesses said.
"They attacked our defence position at K4 and we chased them... There are no casualties from our side," a spokesman for the AU force, Amisom, said.
Hussein Aden, a grocer at Mogadishu's main Bakara market, said he saw eight bodies lying in the street after three mortars detonated nearby.
"The first one landed in front of a shop killing four people and wounding four others who were busy buying vegetables," he said.
Four children were killed when another mortar landed in front of their house, he said.
Six people out of at least 35 civilians who were injured in the clashes later died, hospital sources said.
Fighters loyal to the ICU have launched a series of attacks on AU peacekeepers and their bases since last year.
Nearly 10,000 civilians have been killed in violence in Somalia over the past year, while eight AU soldiers have died. The fighting has also displaced more than one million people.
Ethiopian forces are in Somalia to support the country's UN-backed interim government, which has so far failed to keep control of the country.
Meles Zenawi, Ethiopia's prime minister, said on Thursday that his forces would remain in Somalia until all 8,000 peacekeepers promised by AU members have been deployed.
There are currently about 3,000 troops from Uganda and Burundi operating in Mogadishu.