At least four people have been killed in the attacks.
Al Jazeera’s Zeina Khodr, reporting from Kabul, said that Wardak had been travelling in the second car of a convoy and that four of his bodyguards died with him. Three more were wounded.
“The Taliban says that governors are high-profile targets for them and it should be a lesson to others working with what they call an illegitimate government in Afghanistan.
“The Taliban has repeatedly tried to kill governors.”
Abdul Razaaq, police chief of the district, said the bomb was remotely detonated as the governor’s vehicle passed at 8am (03:30 GMT).
Logar province has seen a rise in Taliban activity in recent months, including the killing of three female Western aid workers on August 14 and their Afghan driver.
“Logar neighbours Kabul and it is a new front line,” Khodr reported. “The Taliban does have a strong presence in the area, along with Gulbuddin Hekmatyar’s Hezb-e-Islami group.
“You feel it’s a very dangerous area, and the government presence there is very weak. You see banners saying ‘Death to America’ and ‘The police is our enemy.’ Some say the Taliban is really getting closer to the capital.”
Wardak was the first provincial governor to be killed since the assassination of Hakim Taniwal, the governor of eastern Paktia province, in September 2006.
During the 2001 US-led invasion to force out the Taliban, Wardak commanded one of the armed Afghan groups fighting with the US military.
Wardak had been a commander in one of several resistance factions fighting against the Soviet invasion in the 1980s. Between 2002 and 2004 he was the minister for martyrs and the disabled in the transitional Afghan government.
Nearly 3,000 people have been killed in fighting in Afghanistan this year, the bloodiest period since the Taliban movement was forced from power.