The pair even hitched a lift to the main gate of the base aboard a military truck, one local official told AFP.
The escape will raise new questions about the capacity and professionalism of the Afghan army as the remaining 100,000 foreign troops in the country prepare to leave next year.
The soldier was arrested last Tuesday after opening fire on foreign troops. The NATO soldier, from Slovakia, died and six other soldiers were wounded in the attack at a military base in the southern province of Kandahar.
"An Afghan army soldier who opened fire on Slovakian soldiers last week has run away from detention," General Abdul Hameed, the top Afghan army commander in the south, told AFP.
The general said another soldier, who had guarded his prison cell, assisted his breakout and also absconded.
The pair managed to sneak off the base by pretending that the detainee was sick and needed to be taken to a military hospital, the general told AFP.
The US-led International Security Assistance Force said it had "full confidence" that the soldier would be re-arrested.
General Zahir Azimi, spokesman for the Afghan defence ministry, said an investigation had been launched.
The Taliban said the shooter, whom they named as Isanullah, had links to them and was helped by a fellow soldier to escape.
"To avoid trouble for him we didn't reveal at the time that he had links with the Taliban... Now as he has escaped and safely joined the mujahedin he was welcomed by the mujahedin," the militants said in a statement.
"The driver agreed without realising their identity. They simply walked off the base and disappeared," he said on condition of anonymity because he was not authorised to speak to the media.