Officers said the assailant walked into a crowd of people enjoying tea under the shade of a tree, before detonating a device at around 3:30 pm (1230 GMT).
"The apparent casualty information we have is the death of seven people, including police and civilians, and six people were wounded," a police statement said. "The explosion occurred under trees where residents of the area spend time to rest," it added.
Witnesses said rescuers rushed to the scene after the blast. "There were dead bodies and wounded people strewn under the trees, the whole area was in a mess," witness Ahmed Adan told AFP, describing how people tried to help the injured.
"This was horrible, the explosion occurred as people were spending time, some of them enjoying with their tea," said another witness, Mohamed Salad.
A renowned Somali poet was believed to be among the dead, according to those at the scene. The Al-Qaeda-linked Al-Shabaab Islamist militant group claimed responsibility for the bombing in a statement.
Al-Shabaab has carried out numerous attacks in Mogadishu and other parts of the country, as the government presses on with an offensive aimed at eradicating the jihadists. In August, at least 37 people were killed in an Al-Shabaab attack on a busy beach in the capital, prompting demonstrations against the group.