"Somalia has today lost a committed parliamentarian who worked tirelessly to serve the people of Somalia and help rebuild our country," Prime Minister Abdiweli Sheikh Ahmed said in a statement, referring to slain MP Isak Mohamed.
The attack comes as the government holds a security conference hoping to tackle continued attacks by Al-Qaeda-linked Shebab insurgents.
"This cowardly attack will not derail the progress made in Mogadishu and across Somalia," Ahmed added.
His colleague and fellow MP Mohamed Abdi was wounded.
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"The explosive device was attached to the car of the lawmaker... We are investigating and hunting the perpetrators to bring them to justice," said Abdukadir Mohamed Abdukadir, commissioner of the Hamarweyne district.
Witnesses said the lawmakers were driving when the explosion occurred.
"The car went off as it was passed by... One of them burned to death, the other one was seriously injured," said Mohamed Adam, a witness.
No one immediately claimed responsibility for the attack, but AU representative for Somalia Mahamet Saleh Annadif condemned the killing and pointed the finger of blame at the Islamists.
"We will continue to fight these extremists who are interested in inflicting violence on innocent civilians," he said in statement.
Somalia's political elite are also divided along rival clan lines, and factional infighting is common.
The blast comes a day after Somali President Hassan Sheikh Mohamud opened the three-day security conference, where he claimed that the "culture of lawlessness that has plagued Somalia for the last 23 years is coming to an end."