"I have counted 10 dead people and 15 others injured. My shop is completely destroyed. The blasts took place in four places in the center of the market," Hassan Ali, a trader at the Bakara market said.
It was not immediately clear who was responsible for the blasts but Islamist group al-Shabab frequently carries out bombings in Somalia and elsewhere.
The government was not immediately available for comment.
Bakara, Mogadishu's largest market, teems with traders and is where most residents buy their food, clothes, medicine, electronics and other items daily.
Residents said several blasts went off, destroying many shops. Three nurses at Erdogan Hospital in Mogadishu said over 20 injured people had been brought to the facility.
Al-Shabab has been battling Somalia's federal government and an African Union mandated peace keeping force for years seeking to establish a new government based on its own interpretation of sharia law.