Hundreds more were wounded when a lorry packed with explosives detonated near the entrance of a hotel.
It is the deadliest terror attack in Somalia since the Islamist al-Shabab group launched its insurgency in 2007.
It is not clear who staged the bombing, but Mogadishu is a target for al-Shabab militants battling the government.
President Mohamed Abdullahi "Farmajo" Mohamed has declared three days of mourning for the victims of the blast.
Local media reported families gathering in the area on Sunday morning, looking for missing loved ones amid the ruins of one of the largest bombs ever to strike the city.
Police official Ibrahim Mohamed told AFP news agency the death toll is likely to rise. "There are more than 300 wounded, some of them seriously," he said.
Officials also confirmed that two people were killed in a second bomb attack in the Madina district of the city.