(CNN) -- Militants who control parts of Somalia's capital city are beating women in broad daylight for violating their radical brand of Islamic law, according to local officials and witnesses in Mogadishu.

"Just today, Al-Shabaab dispatched men with whips to the streets around Bakara market and they are flogging any woman who is found not wearing socks," according to a female maize trader at the Mogadishu market, who spoke Thursday.

She did not want to be named for security reasons.

In the past two days, more than 130 people, including women who were not wearing headscarves and men chewing dried khat leaves, have been detained for violating Al-Shabaab's interpretation of sharia, or Islamic law, according to witnesses and officials.

Hooded Al-Shabaab gunmen rounded up 50 women on Wednesday from Mogadishu's Bakara market for not wearing the veil that is required for women under some interpretations of Islamic law, according to the maize trader.

"Most of these women were vegetable traders, so they are poor and can't afford to buy veils for 600,000 shillings [about $23 U.S.]," she said.

She said she saw more women being detained Thursday.

Another 80 Somali civilians were detained in the southwestern town of Luuq, near the Kenyan and Ethiopian border, "because they turned deaf ear to orders we imposed on the town," said the local Al-Shabaab commander Sheikh Hussien al-Iraqi.

Al-Shabaab is considered a terrorist organization by the United States because of its ties to Osama bin Laden's al Qaeda network.

It has been imposing stricter rules on Somali civilians living in the areas it controls.

Earlier this month, Al-Shabaab militants whipped women for wearing bras in an area of northern Mogadishu that they control, shocking residents who have been besieged by the ongoing insurgency. The militants believe the female undergarments are a deception to men.