This was just one of the latest violent incidents in a Middle Eastern country that has become a proxy battleground for Saudi Arabia and Iran, as well as a target for Islamist groups like ISIS and al Qaeda in the Arabian Peninsula.
Two schoolchildren and a number of security troops were among the dead, and at least six other people were injured, three senior Aden security officials said.
Among the injured was a Yemeni general; he was in critical condition, a senior Aden security official said.
The three security officials said Hadi was not hurt, but their information about his whereabouts conflicted. Two of the officials said Hadi was inside the palace when the attack happened, but the third said he had left the palace Wednesday to an undisclosed location.
In a statement posted online, ISIS claimed that one of its fighters was Thursday's suicide bomber.
Aden eventually became a headquarters for Hadi after Houthi rebels, who are Shiite and allied with Iran, ousted Hadi's Sunni-led government from the capital, Sanaa, in January 2015.
A coalition of nations led by Yemen's northern neighbor, Sunni-dominated Saudi Arabia, have launched airstrikes against rebel targets in support of Hadi since March.
Thousands of civilians have been killed in the violence.
The Saudi-led coalition, which includes the United Arab Emirates, Kuwait, Bahrain, Qatar and other countries, has launched airstrikes on Houthi positions in Yemen since March 2015, with a brief truce last summer.
More than 2,800 civilians have been killed and thousands more have been injured since the war began, the United Nations has said.
After Saudi-led coalition forces defeated the Houthis in Aden in July, militants affiliated with rival terror groups ISIS and al Qaeda launched attacks in the city.
At least 32 government officials in Aden have been killed by militants over the last two months, including Aden's former governor, who was assassinated in early December. ISIS and al Qaeda have claimed responsibility for most of those attacks.