"A young man has just been lashed 40 times for drinking alcohol. The whipping took place in the Timbuktu market," a resident told AFP by phone.
"He is injured and was taken to hospital," the resident added, asking not to be identified.
Other witnesses confirmed the incident.
The Islamist group, Ansar Dine (Defenders of Faith), is one of several Al-Qaeda-linked groups that seized northern Mali amid a power vacuum opened by a March 22 military coup in the south.
The groups have been imposing sharia throughout their territory, and aim to spread the strict Islamic law to the rest of Mali.
A man and woman accused of having a child out of wedlock were given 100 lashes each in Timbuktu on June 20, and Ansar Dine has destroyed all the city's bars.
The group has also demolished most of the ancient city's shrines to Muslim saints, which the jihadists consider idolatrous.
Another Islamist group, the Movement for Oneness and Jihad in West Africa (MUJAO), has burnt cigarettes, whipped smokers and forbidden people to play football or watch television in territory under its control, provoking violent protests in May in the northern city of Gao.