Agha Lala Dastageri, Kandahar's deputy provincial governor, said Gen. Abdul Raziq, a powerful provincial police chief, and intelligence chief Abdul Mohmin died immediately in the attack, and Zalmay Wesa, the province's governor, died in hospital.
Taliban spokesman Qari Yousuf Ahmadi took responsibility for the attack.
The NATO-led Resolute Support Mission in a statement confirmed the incident and said two Americans have sustained injuries but the RS and USA forces Commander Gen. Scott Miller has escaped the attack unhurt.
North Atlantic Treaty Organisation spokesperson Colonel Knut Peters said Miller, who took command of US and forces and the NATO-led Resolute Support mission in Afghanistan last month, was uninjured.
Provincial police spokesman Salam Afghan confirmed the explosion had killed one person and wounded at least two. "We are being told the area is secure".
An Afghan lawmaker contesting this week's parliamentary elections was among four people killed on Wednesday by a bomb planted under his office chair, officials said, in an attack claimed by Taliban militants.
The Taliban claimed responsibility for the attack on Qahraman, who was running for the southern province of Helmand, a stronghold for the militant group, reported AFP.
Three Americans, including a soldier, civilian and contractor, were wounded in the cross-fire and had been evacuated from the scene.
A controversial but influential Afghan police chief has been shot dead days before parliamentary elections, leaving a gaping power vacuum in the Taliban's birthplace. Ahmadi asserted that Miller had been killed, a claim denied by USA military officials.
The three Afghan officials were all severely wounded when the gunman opened fire and two members of Miller's protection detail were also hit in the crossfire but Miller, who took command of US forces in Afghanistan and the NATO-led Resolute Support mission last month was not injured.
He continued: "The incident will also make the military balance in southern Afghanistan considerably more fragile, as General Raziq was often at the forefront of government efforts to slow the Taliban's advances".
Afghanistan is on high alert ahead of the long-delayed legislative elections, scheduled for October 20, after the Taliban pledged to attack the ballot.
Another witness said the city was "full of military forces". He ruled in Kandahar, the former Taliban heartland, with an iron fist and had survived several attempts to kill him, including one previous year that resulted in the death of five diplomats from the United Arab Emirates.