The Somali government claimed the cargo, which was offloaded at Mogadishu International Airport under heavy security, was an assortment of weapons from Eritrea.
But the Islamist militia, which controls the airport and the capital Mogadishu, has refused to comment on the contents.
The Russian-made Ilyushin 76-cargo plane was met by two senior Islamic commanders. Another member of the Supreme Islamic Council of Somalia (SICS) said the aircraft carried weapons from an undisclosed origin.
It was earlier thought that the plane's tail bore the Somali national flag, a white star on a blue background, but officials said it was the emblem of Kazakhstan. The Kazakh flag has a gold emblem on a blue background.
The plane landed at about 8:00 am (0500 GMT) and left for an unknown destination two hours later after the cargo was offloaded, witnesses said.
Journalists were chased away from the facility by armed militia,
"Military supplies from Eritrea have reached Mogadishu. They include explosives, mines, hand-propelled grenades, bazookas and anti-tank/aircraft missiles," deputy information minister Salad Ali Jeeley told reporters in
Baidoa.
The town is the temporary base of Somalia’s government, about 250 kilometres northwest of the capital after Islamic militia won a battle over US back warlords for control of Mogadishu.
Weapons dispute
"We call upon the international community including IGAD (Inter-Governmental Authority on Development) to witness what is happening in Somalia and Eritrea's intervention," he said. "The government condemns the Eritrean intervention."
But the Supreme Islamic Council of Somalia insisted that the airport was open for civilian use.
"The Mogadishu airport and all other airports are open and those who want to use the facility have the right to do so. I am not in charge of cargo and you have no right to ask me what was the shipment. I don't want to speculate," SICS security chief Sheikh Yusuf Mohamed Siad told reporters.
Asked about the government claim that the cargo was weapons, he said: "Go and ask Eritrea if you want to say something about them. What I can say is that the plane has landed and taken off safely."
The Islamists are at loggerheads with the government over the deployment of Ethiopian troops to protect the fragile government.
The government and the largely Ethiopian Christian regime have rejected the incursion claims, arguing that the SICS was looking for an excuse to wage war and expand its territory.