Some reports said bombs were packed in cars that exploded simultaneously, others that a truck or tanker was used.
The explosion struck close to the offices of the Kandahar provincial council, trapping people under rubble.
Windows across the city were shattered by the force of the blast.
The area has several hotels and offices of non-governmental organisations.
A wedding hall was one of the buildings damaged, along with the headquarters of a Japanese construction company.
MAJOR ATTACKS THIS MONTH
18 Aug: Nine Afghans and a Nato soldier die and more than 50 are injured in Kabul
15 Aug: Suicide bomb outside Nato HQ in Kabul kills seven and injures 90
13 Aug: Twin blasts in Helmand and Kandahar kill 14, including several children
6 Aug: Five American and three UK soldiers, five civilians and five policemen killed by roadside bombs mainly in Helmand
3 Aug: Bomb in city of Herat kills 12
1-2 Aug: Nine foreign soldiers killed over weekend
Afghans are currently observing the Muslim month of Ramadan and the explosion took place soon after dusk as they broke their fast.
Agha Lalai, a member of the Kandahar provincial council, told AFP news agency: "It felt like an earthquake. The power went off and there was a huge explosion. Police have cordoned off the area and are busy with the wounded."
Deputy provincial police chief Mohammad Sher Shah told the Associated Press news agency: "Once again they've killed children, women, innocent Afghans. They are not human. They are animals. You can see for yourself the destruction of this enemy."
There have been a series of insurgent attacks across the country as Afghanistan held its presidential election.
The Nato-led International Security Assistance Force (Isaf) said there were more than 400 attacks on election day alone, last Thursday.
The four US soldiers who died were killed "while patrolling in one of the most violent areas of Afghanistan", Nato spokesman Brig Gen Eric Tremblay said, without giving an exact location.
The deaths brought the number of foreign forces killed in Afghanistan in 2009 to 295.
The previous deadliest year was 2008, when 294 military personnel died.
More than 30,000 extra US troops have been sent to Afghanistan since President Barack Obama ordered reinforcements in May, almost doubling his country's contingent and increasing the Western total to about 100,000.
The first results in the presidential poll, announced on Tuesday, gave incumbent Hamid Karzai a slender lead over former foreign minister Abdullah Abdullah, by 40.6% to 38.7%.
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