The group said it carried out the attack and said more would follow.
Meanwhile, two people are said to have been killed in Mogadishu during protests against a deal to extend the terms of the president and parliament.
Under the deal signed in Uganda on Thursday, their mandates have been extended until June 2012 and the prime minister is to be sacked.
Friday saw a second day of demonstrations in support of Prime Minister Mohamed Abdullahi Farmajo.
Witnesses said troops fired on the protesters, who had gathered outside the hotel where MPs have been meeting.
Losing ground The attack against Sheikh Hassan was the third suicide attack in Mogadishu in three weeks.
His niece had visited his home several times in recent days and the guards did not carry out a security check.
She walked into the home, set off the bomb, and was killed instantly.
The minister died from his injuries as efforts were under way to fly him for treatment in neighbouring Kenya.
In recent months al-Shabab - which has links with al-Qaeda - have lost territory as Somali government troops and African Union soldiers have been on the offensive.
BBC East Africa correspondent Will Ross says that when al-Shabab has appeared to be militarily weak in the past, it has targeted high-profile government officials.
The group still controls much of southern and central areas of the country.
Somalia has been torn apart by constant war for more than 20 years. Its last functioning national government was toppled in 1991.