Addow was the third senior government figure to have been killed in as many days, after the security minister died in a suicide attack in the western town of Beledweyne and a senior police officer was killed in fighting in the capital.
"This is yet another terrorist attack, only hours later," Mohamed Dhere, Somalia's deputy transport minister, said.
Al-Shabab, which has allied with the Hizbul Islam movement, said one of its fighters crashed his vehicle into the hotel in Beledweyne on Thursday, killing Omar Hashi Aden and at least 19 other people.
In May, the two groups launched an offensive against the transitional government, which has little effective control over much of the country.
The fighting has claimed the lives of around 300 civilians and has caused more than 120,000 people to flee Mogadishu since then.
Mohamed Omaar, Somalia's foreign minister, told Al Jazeera on Thursday that al-Shabab's offensive had "failed completely".
"We have pushed them back," he said.
Omaar said the government would be able to hold on to its gains in Mogadishu because "the Somali public are tired of twenty years of conflict and are in favour of peace".
Somalia has not had an effective government since 1991 when Mohamed Siad Barre, the former president, was overthrown, plunging the country into chaos.
Kenya's foreign minister warned on Friday that the worsening situation in Somalia was a threat to stability across the region.
"We will not sit by and watch the situation in Somalia deteriorate beyond where it is. We have a duty ... as a government to protect our strategic interests including our security," Moses Wetangula said.
Wetangula also urged countries who had pledged a total of $213 million to build up security forces to deliver on those pledges as soon as possible.
"The government in Mogadishu needs to operate, they need the funds to pay their civil services, their outgoings in many waysand they need survival kits, they are under immense pressure from the rebels that are fighting them," he said.