Ali Nur, a police officer, told Reuters on Wednesday: "Every policeman and government soldier has orders to confiscate veils from veiled women."
He said the order had been issued after several recent attacks had been carried out by people in disguise.
"Some of the remnants of the Islamic Courts have been caught wearing veils. During the war, these remnants, pretending to be women, killed so many government troops."
Most Somali women traditionally cover their heads but leave their faces unveiled.
Officials say some suicide attacks have been carried out by men disguised under full face-veils, known as indhasharer in Somali.
A Reuters witness saw several veiled women running away from police on Wednesday.
Near the main Tarbuunka Square, a Somali woman was seen removing her face covering before approaching a government checkpoint where one soldier clutched several of the black veils, which cover the face and leave only the eyes visible.
Mogadishu residents said government troops and police had been forcibly removing face veils and publicly destroying them.
A senior cleric, who declined to be named for fear of reprisals, urged the government to be sensitive.
"If the government is unveiling women out of security concerns, then I think it is acceptable. However, this can raise public anger," he told Reuters.
"The government has to undertake it very carefully. They should use women to frisk and unveil women, not men."
Also on Wednesday, government and Ethiopian troops handed over quantities of captured weapons, including anti-tank mines and rocket-propelled grenades, to African Union peacekeeping troops, saying they were seized from a fighters' stronghold overnight.