A car bomb went off first outside the Village restaurant about 11 a.m. Saturday followed by a suicide bombing at the same restaurant, The New York Times reported.
"This is actually very shocking, losing colleagues who were healthy just minutes ago." said Awale Geedi, an engineer who was nearby when the first blast happened. "These continued attacks are unacceptable. The government has to do something to change the situation."
The Islamist militant group al-Shabaab has claimed responsibility for the attacks.
"We condemn this terrorist attack targeted at innocent Somali civilians meant to endanger the security gains," Foreign Minister Fowziya Yusuf Aden said in a statement.
Al-Shabaab attacked the same restaurant last year in a suicide bombing, killing 14 people. The group also attacked the Lido Seafood restaurant at Lido Beach with a remotely detonated car bomb in February.
"Such cruel and cowardly acts of terrorism serve to remind us that the people of Somalia desperately need peace," Nicholas Kay, the U.N. special representative for Somalia, said in a statement.