Al Jazeera's correspondent in Afghanistan, James Bays, said the attack was the Taliban's revenge for the killing of commander Mullah Dadullah earlier this week.
Earlier, two bombs tore through the Kandahar about 30 minutes apart, killing seven police officers and security guards, police said.
Ismatullah Alizai, Kandahar's police chief, said the first blast struck the vehicle of a private security company, killing four of the guards.
The interior ministry later identified the firm as US Protection and Investigation (USPI) company. It gave the same toll.
Texas-based USPI is one of the biggest security firms in Afghanistan.
About half an hour later, as police and reporters gathered at the site, a second bomb exploded metres away.
The ministry said: "It took place as the security chief with his investigation team arrived at the site.
"The explosion killed three, including a police officer and two policemen."
A policeman at the scene, Mohammad Jan, said four officers were wounded including the security chief, who is also the deputy provincial police chief, Abdul Hakim Angar.
An Al Jazeera news producer was slightly wounded.
Both bombs were remotely detonated, the interior ministry said in a statement.
Qari Yousef Ahmadi, a purported Taliban spokesman, said on Thursday that the co-ordinated bombings were planned to hit police responding to the first blast.
|Police officers gather at the site of Thursday's|
blasts in the centre of Kandahar city [AFP]
Mullah Dadullah, the Taliban field commander, was killed during a US-led operation in neighbouring Helmand province.
The Taliban had warned of "bad consequences" if the government did not hand over Dadullah's body to his relaives.
Kandahar's governor has said that Dadullah was buried at a secret location near Kandahar.
In another attack on Thursday, a remote-controlled bomb struck a vehicle of the provincial police chief of the northern province of Badakhshan, killing a guard and wounding the officer and his aide, the interior ministry said.
A provincial official blamed the attack on the "opposition forces".
Also early on Thursday, Pakistani and Afghan troops exchanged mortar and gun fire on their disputed border, days after clashes on the frontier killed more than a dozen people, a Pakistani official said.
The two-hour battle started after Afghan forces fired a mortar at Pakistani soldiers near the Teri Mangal area in the Khyber tribal district, a Pakistani military spokesman said on condition of anonymity.
"Pakistani forces responded effectively and the exchange of fire continued until 5am local time. There were no casualties on the Pakistani side," the spokesman said.
There was no immediate response from the Afghan authorities.
The clash was near an area where a US soldier and a Pakistani trooper were shot dead on Monday after a meeting, also involving Afghan officials, that was aimed at calming tensions.
Afghan officials meanwhile accused Pakistan of starting clashes in the same area on Sunday that continued into Monday, saying Pakistani troops pushed 4km over the disputed border.
Pakistan denied the charge.
Thirteen Afghans were killed in the fighting, which included rocket fire, Afghan officials said.