Prime Minister Ali Gedi, who escaped unhurt, said the blast on Tuesday appeared to have been an accident.
A security official said a militiaman guarding Gedi had detonated one of his grenades.
"I am very sorry for what happened at the stadium. It is an unexpected accident and I send condolences to the relatives," Gedi said.
Gedi flew to Mogadishu on Friday for the first time since his appointment last year, seeking to end a rift in his government over the location of a future capital and the role of UN peacekeepers in the strife torn country.
Lawlessness has continued to plague Mogadishu despite the formation of President Abdullahi Yusuf's Transitional Federal Government in exile in neighbouring Kenya last year - the 14th attempt at government formation in nearly as many years.
Colonel Abdi Hasan Awali, the police chief in the last government who is working with Gedi's security officials, said seven people were killed in Tuesday's blast.
Witnesses and hospital officials said three others had died on their way to or at the hospital and another was killed by a vehicle leaving the scene.
Awali said a militiaman hired to protect Gedi's entourage appeared to have been responsible for the blast.
Conflict in Somalia has created
tens of thousands of refugees
"It was an accident that happened after one of the private militiamen's grenades exploded," Awali said.
Witnesses said the blast tore through a stadium wall and left blood everywhere. Officials at four hospitals said a total of 57 were wounded.
But one aide of the prime minister made a conflicting claim.
"As far as we are concerned it was a bomb. Nobody knows who did it, the reason or motivation behind it," political adviser Abd al-Rahman Ali Usman said.
The new government has come under growing pressure from foreign governments and donors to return home, although the country is still a patchwork of fiefdoms run by armed faction leaders.
The lack of safety in Mogadishu has been the main argument made by Gedi and his parliamentary allies against moving the government back to the capital.
Gedi and deputies aligned with him would prefer first to relocate from Nairobi to the relatively safer Somali cities of Jowhar or Baidoa.