The body of Buri Mohamed Hamza, minister of state in the prime minister's office for the environment, has been retrieved from the collapsed building of the Naasa Hablood hotel, the ministry added.
"We extend our deepest condolences to the relatives of the minister who was killed in Mogadishu yesterday," a ministry statement read.
Yesterday's assault, the latest in a series by the Islamist group targeting hotels and restaurants, began when a suicide bomber detonated a car laden with explosives outside the building.
Two of the 11 dead were doctors, a security ministry spokesman said, while medical sources said some 20 civilians were wounded.
Also Read
The Shabaab claimed responsibility for the attack through a statement on the Telegram smartphone app, saying their fighters had forced their way into the hotel.
The assault came three weeks after another attack quickly claimed the Shabaab group on the city's Ambassador hotel left 10 dead including two lawmakers when a huge car bomb ripped the front off the six-storey building.
In recent months they have also claimed attacks on bases of the African Union peacekeeping mission in Somalia (AMISOM).
The Shabaab lost their foothold in the capital in 2011 but continue their battle to overthrow the Somali government and launch regular attacks on military, government and civilian targets like hotels and restaurants in Mogadishu and elsewhere.