"A massive operation is under way to find the escaped inmates," he told the AFP news agency.
"The Afghan security forces are searching for them within the city and along the main and secondary roads."
None of the escaped inmates have been caught yet, Hashimzai said.
Large numbers of security forces, including those of from the US-trained Afghan national army, have been deployed to search vehicles, AFP reports.
Brigadier General Carlos Branco, a spokesman for Nato's International Security Assistance Force (Isaf), said: "Afghanistan national security forces and Isaf forces have cordoned off the area to re-establish security and recapture the escapees."
"We admit it, their guys did the job properly in that sense, but it does not have a strategic impact," he said.
The attack came a day after world donors gathered at a conference in Paris and pledged $20bn to rebuild Afghanistan but also called on Hamid Karzai, the Afghan president, to strengthen security.
Yousuf Ahmadi, a Taliban spokesperson, said the fighters used suicide bombers and detonated a bomb-laden water tanker as part of the attack.
"First we exploded two suicide attacks and then our mujahidin (holy warriors) riding motorcycles entered the prison and killed the remaining security guards," Ahmadi said.
|A signed Taliban statement claimed the group|
planned the operation for two months[AFP]
"We successfully freed all prisoners, including jailed Taliban and other prisoners."
A statement posted on the Taliban website later said about 400 Taliban-linked fighters and several hundred other inmates were freed from the prison.
The statement, signed by Ahmadi, said the Taliban had planned the attack two months ago.
Hashem Ahelbarra, Al Jazeera's correspondent in Afghanistan, quoted witnesses as saying a vehicle carrying an attacker blew up near the prison gate before other fighters joined the battle and killed the guards.
"We saw a man driving a truck smash into the entrance of the jail then there was a huge explosion ... a shooting rampage followed," one witness said.
"We have seen prisoners flee under huge fire cover from the attackers. There was chaos and confusion. My brother who was passing nearby was killed," he said.
Mark Laity, a Nato civilian spokesman, told Al Jazeera: "The release of a significant number of Taliban members is something of a setback."
"They managed to launch this attack and they succeeded, obviously we will have to learn lessons and we'll have to check to make sure that something like this doesn’t happen again.
"It is an increased security problem, this is an extra problem for us but I don’t want to overstate it. This is a bad day but this is not a bad year," he said.
Kandahar jail was the scene of a mass hunger strike by hundreds of inmates in May, during which 47 of the prisoners sewed their lips shut after complaining they had been tortured and denied fair trials.
Prisoners, including al-Qaeda and Taliban fighters, rioted at Afghanistan's main Pul-e-Charki jail, in the capital Kabul, in February 2006, taking control of a block and leaving several people injured.