The blast occurred in Mogadishu's Hamarweyne district, a busy area with shops and restaurants.
"Several dead people were removed from a wrecked building at the blast scene. So far [the] death toll is 11 civilians and 10 others injured," police officer Mohamed Hussein told Reuters news agency.
A witness saw one dead person at the scene, where four cars were burned out and a restaurant destroyed.
Al Shabaab is an al-Qaeda-linked armed group fighting to overthrow the country's western-backed government and establish its own rule based on a strict interpretation of sharia law.
It frequently carries out bombings in Mogadishu and other parts of Somalia against government and other targets.
In late December 2018 seven people were killed in two bomb attacks in the capital.
Al-Shabaab fighters killed
The car bomb comes just three days after least 13 Shabaab fighters were killed in a US Africa Command (Africom) airstrike 48 kilometres south of Mogadishu.
In a statement issued on Saturday, Africom said "US Africa Command currently assesses this airstrike killed thirteen militants. At this time, it was assessed no civilians were injured or killed in this airstrike".
Al-Shabaab's militants also carry out attacks outside Somalia. Its latest assault in neighbouring Kenya, a suicide and gun attack at an office and hotel complex in the capital Nairobi last month, killed 21 people.
Al-Shabaab want Kenya to withdraw its troops from Somalia where they are stationed as part of an African peacekeeping force which helps defend the central government.