The exodus came as the International Committee for the Red Cross on Saturday asked the warring parties to protect civilians caught up in the conflict there.
A mother of five, Sahro Ali Mohamed, said houses in her Mogadishu district were deserted.
This week has seen some of the heaviest fighting in the capital since late December when the Union of Islamic Courts movement was driven out by the interim Somali government and its Ethiopian allies.
Somlia is anxiously awaiting the deployment of an 8,000-strong African Union force to try to help the transitional government restore order in Mogadishu.
The deployment was approved last Tuesday by the UN Security Council.
But the AU has so far managed to raise only half of the required peacekeepers, with possible troop pledges from Nigeria, Burundi, Malawi and Ghana as well as Uganda, which has offered 1,500 troops.