Al Jazeera's correspondent also reported that one police officer has been killed and several others injured in a bomb attack on a police station in southern Mogadishu later on Sunday.
Abdikadir Adan Shire, the transitional government's defence minister, said: I understand some of the senior officials are among the wounded."
"I also hear people died, but we do not have a full report yet," he added.
Thousands of people had gathered for the ceremony when the explosion occured.
"There was a blast and people started running for their lives, all shouting 'bomb!, bomb!'," Mohamed Daud, who was in the crowd, told Reuters news agency.
"Police started firing in all directions ... Most of the wounded are civilians."
Troops sealed off the park where the rally was being held after the explosion while some soldiers opened fire on the streets.
Kismayo was the last major city held by the Islamic Courts Union that controlled much of south and central Somalia until it was forced out by Ethiopian and Somali transitional government troops in January.
The Islamic courts has vowed to wage guerrilla war and there have been near-daily mortar, rocket and gun attacks since its forces fled.
Kismayo has been relatively peaceful but three weeks ago unidentified men shot dead an Ethiopian soldier and wounded another in a shootout in the port.