Minister Yusuf Mohamed Siad was abducted as he walked out of a mosque in Kampala, Somali government spokesman Sheik Abdirisaq Qeylow said.
"We are investigating," Qeylow told The Associated Press. "All we know so far is that he was taken away."
Calls to authorities in Uganda were not immediately returned.
Somalia has been ravaged by violence and anarchy since warlords overthrew dictator Mohamed Siad Barre in 1991, then turned on each other. The al-Shabab insurgent group, which has foreign fighters in its ranks, operates openly in the capital and seeks to overthrow the government and impose a strict form of Islam in Somalia.
The circumstances of the kidnapping were not immediately clear. Kidnappings for ransom are common in Somalia, where the government controls just a few blocks of the capital. Uganda provides many of the troops for a 5,000-strong African Union peacekeeping force in Somalia.