According to BBC Pashto service, the banned terrorist group Baloch Liberation Army (BLA) confirmed the death of Aslam along with other terrorists.
A child was also injured in the attack in the second largest city of Afghanistan.
Sources said the other terrorists killed in the attack included; Taju Marri, Rustom alias Rosto, Rahim Marri and Nasir Baloch.
The local sources told BBC that Aslam had arrived in Kandahar a few weeks back.
According to Pakistani sources, Achhoo was the mastermind of the recent attack on the Chinese consulate in Karachi and he was also behind an attack on the Quaid-i-Azam Residency in Ziarat. He was the chief of a group of the BLA.
They said Achhoo was taken to India via Afghanistan for treatment after he was injured in an earlier incident. He had returned to Afghanistan after recovery.
Afghan authorities said the attack took place in Eeno Meena, a posh area of Kandahar. No group has claimed responsibility for the suicide attack so far.
Cases of bomb explosions, attacks on security forces and target killing had been registered against Aslam and his head money was fixed at Rs5 million.
According to the banned BLA’s statement, Aslam was one of the founding leaders of the organisation and had been associated with it for 25 years. It said other terrorists killed in the attack had also been associated with the group for several years.