"We heard a big explosion, which seemed to be a landmine targeting the car," Abdirahman Ali, a witness, said. "I was standing opposite. Bodyguards opened fire."
Omar spoke to the media shortly after being treated for shoulder injuries at a Mogadishu hospital.
"I have no problem and I escaped the attack," he said.
"I'm not going to say who is behind the attack just now but we all know each other in the capital Mogadishu and we will take steps to enforce peace."
Somalia's transitional government has little control in the war-torn country, which is dominated by rival armed Islamic groups and has been without an effective central government since 1991.
However, there are tentative hopes for some sort of stability under the new government under Sharif Ahmed, the president and a former leader of the Islamic courts union, which ruled much of the country in late 2006.
"Because the war has been fought for so long, the suffering is so long that people are crying for peace," Ahmedou Ould-Abdallah, the UN envoy to Somalia, said.
"The government has to strengthen its base and simultaneously reach out to all Somalis."
Omar led a Somali group fighting Ethiopian troops, who helped push the Islamic courts out of Somalia in 2006, before was appointed to the interior ministry following a deal to bring the armed opposition into government.
Al-Shabaab, a hardline group which controls several towns, including the government's former seat in Baidoa, launches frequent attacks on government targets and African Union peacekeepers.