Abdi Nur Hassan, a market trader, said two missiles landed near his electronics stall.
"I have seen six people die, some of them missing legs and hands. We collected their bodies, but it is difficult to separate them," he said.
Abshir Mohamed Ali, a shop owner, told The Associated Press news agency: "There is blood everywhere, and human flesh on the walls."
Dahir Dhere, director of Mogadishu's main Madina hospital, said more than 60 wounded civilians had been admitted following the incident.
In the past, government officials have said they suspect anti-government fighters of using the market as a base.
"When troops die
in attacks they [government forces] target civilians like ... at Bakara Market today"
The al-Shabaab armed group, an offshoot of the Union of Islamic Courts which controlled much of Somalia in 2006, said that government and Ethiopian troops had targeted the Bakara market.
"When troops die in attacks they [government forces] target civilians like ... at Bakara Market today," Muktar Roboow, an al-Shabaab spokesman, told the Reuters news agency.
However, Abdulahi Hassan Barise, a police spokesman, said that the clashes began on Sunday after armed men attacked African Union peacekeeper bases in the K$ and Jazeera districts.
"Al-Shabaab militant group attacked government bases and foreign troop bases. They also threw mortars at residential areas ... so al-Shabaab is responsible for all that has happened today and last night," he said.
The fighting came as the transitional government and opposition elements ended their latest round of peace talks in Djibouti.
Armed groups opposed to the government and their Ethiopian supporters carry out near-dailly attacks in the capital.
International aid organisations and rights groups have said that at least 6,000 civilians have been killed as a result of the fighting over the past year alone.