The huge blast also left 10 people wounded, police added.
Bursts of gunfire followed the attack, which targeted the Italian Coffee cafeteria, located near the passport office.
President Mohamed Abdullahi Mohamed, who was elected earlier this year, has declared war against al-Shabaab and said his government will overcome the group within two years.
10+ wounded - Sources pic.twitter.com/6is5MR1xTh- Live From Mogadishu (@Daudoo) 8 mai 2017 vehicle bomb kills at least five people in Somali capital#Somalia #AlShabaab #Mogadishu https://t.co/wqGV0BE9d2 pic.twitter.com/lUBDjVaLMz- Gulf-Times (@GulfTimes_QATAR) 8 mai 2017 Has anyone admitted planting the bomb?
No group has yet claimed responsibility for the attack but Somali insurgent group al-Shabaab has threatened to continue their activities against the internationally recognized government.
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In recent years, the Al Qaeda-linked group has lost large swathes of its territory to African Union peacekeepers supporting the United Nations -backed government.
The Takfiri militant group was forced out of the capital by African Union troops in 2011 but still controls parts of the countryside and carries out attacks against government, military and civilian targets. Have there been other attacks recently? Yes.
The statement by Somalia's information minister said Lower Shabelle regional leader Moalin Osman Abdi Badil and three associates were killed Friday in Bariire village west of the capital, Mogadishu. How long has the conflict in Somalia been going on?
"A suicide auto bomb was driven into the cafeteria before exploding".
"We are behind the blast", Sheikh Abdiasis Abu Musab, the group's military operations spokesman, told Reuters.