Mullah Amanullah was detained near Deh Rawood, a town in Uruzgan province 250 miles southwest of the capital, Kabul (search), provincial police chief Rozi Khan told The Associated Press.
Khan said Amanullah opened fire on Afghan forces who had flooded an area called Sangar after a tipoff and stopped his car. A police commander was killed.
"After that the other police were able to arrest him," Khan said. Three remote-controlled bombs, a satellite telephone and an AK-47 assault rifle were found in the vehicle, he said.
It was not immediately clear what role Amanullah, who like many Afghans goes by one name, held in the Taliban movement or if he had any contact with Omar.
Omar had four wives, each of which could have many brothers if they belong to typically large Afghan families.
Khan said Afghan authorities might hand Amanullah over to U.S. forces, who have a base near Deh Rawood.
Still, American spokesman Maj. Rick Peat said he had no information on the reported arrest.
Deh Rawood has been a focus of the stubborn insurgency maintained by Omar's followers since U.S. forces and Afghan allies pushed them from power in late 2001.
The U.S. military is pulling out a 2,000-member Marine force that has killed scores of militants in Uruzgan and neighboring provinces since May. They are to be replaced by a regular infantry battalion.