The brutal attack in Paghman, outside Kabul, provoked a national outcry with many Afghans demanding the men be hanged, and then-president Hamid Karzai signed their death sentences shortly before leaving office last week.
Five men in connection to the Paghman incident and one other big criminal were executed this afternoon," Rahmatullah Nazari, the deputy attorney general, told AFP.
There was no immediate comment from the office of President Ghani, who faced strong public pressure to not stay the executions after he came to power on August 29.
The men were executed in Pul-e-Charkhi prison near Kabul.
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Franz-Michael Mellbin, the EU ambassador in Kabul, strongly criticised the hangings, and questioned Ghani's failure to intervene.
"Today's executions cast a dark shadow over the new Afghan government's will to uphold basic human rights," Mellbin said on Twitter soon after the news broke.
In August the armed gang members, wearing police uniforms, stopped a convoy of cars returning to Kabul at night from a wedding in Paghman, a scenic spot popular with day-trippers.
But the court process raised major concerns, with the trial lasting only a few hours, allegations of the suspects confessing under torture, and Karzai calling for the men to be hanged even before the case was heard.
In a statement before the executions, the UN High Commission for Human Rights "called on President Ghani to refer the cases back to the courts given the very serious due process concerns".
Amnesty said the trial had been rushed, giving lawyers little time to prepare the defence. It was only nine days between the arrests and the handing down of death sentences by the primary court.
"(Karzai) himself said that he urged the Supreme Court to hand down death sentences.