Salagle District Police Commissioner Hassan Ali Isaaq said thousands of hungry people were gathered in Shiidleey, a village 560 kilometers (350 miles) southwest of the capital, Mogadishu, when the shooting occurred late on Monday.
"An old women died and two other women were injured," he said. "We arrested the militia man."
The World Food Program had been distributing food in the area. After the shooting, eight of 11 food trucks returned to the provincial headquarters, Buale, said the regional militia commander, Col. Duale Ganane Unun.
"We are very sorry that the food was not distributed to all the people, we are persuading World Vision and WFP to send back the food," Col. Unun said.
Nairobi-based WFP spokesman Peter Smerdon said that out of 1,716 people, 282 hadn't yet received their food when the incident occurred, but after the shooting, people looted the remaining food.
"WFP has halted distributions in the area until local authorities can assure us that such incidents will not be repeated," he said.
There have been at least half a dozen shooting or looting incidents during food distributions in Somalia in recent weeks.
Much of Somalia has been wracked by violence since 1991, when rival warlords overthrew dictator Mohamed Siad Barre and then turned on each other. The impoverished country is awash with weapons, and powerful clan-based militias often fight over food aid to deny it to rival clans or steal it for their own fighters.