Afghan officials says the execution for murder of a former military commander does not mean a policy of capital punishment has been reintroduced.
President Karzai will decide the fate of about 20 death-row prisoners
Abdullah Shah was shot at a jail outside Kabul last week after being convicted of killing 20 people.
Jawed Ludin, chief spokesman for President Hamid Karzai, said the case was an exception, not the rule.
"[Shah's] execution cannot be a reason to say that the execution process has started," Mr Ludin said.
He told Reuters news agency it was "premature" to say the execution of Shah meant capital punishment had resumed in Afghanistan.
There are about 20 people in Afghan jails who have been sentenced to death, court authorities told Reuters.
Rights group Amnesty International said it feared Shah's execution "may have been an attempt by powerful political players to eliminate a key witness to human rights abuses".
Shah was shot at Pul-e-Charkhi prison on 20 April
It said Shah was denied even basic standards of fairness.
President Karzai approved the execution although he initially reportedly asked the Supreme Court to commute the sentence to life imprisonment.
He will have the final say over the others on death row.
Abdullah Shah served under another commander, Zardad, in the 1992-96 civil war, and earned the nickname Zardad's Dog for attacks on travellers along the road between Jalalabad and Kabul in the 1990s.
Shah, who was executed at Pul-e-Charkhi jail on 20 April, was convicted of 20 counts of murder in special court proceedings in October 2002.
He was found guilty of killing one of his wives by pouring boiling water over her body.
Another wife, who said he had tried to burn her to death after dousing her with petrol, was one of those who testified against him.
The court heard Shah murdered his baby daughter by banging her repeatedly against a wall, officials say.
Mr Ludin said that in approving the execution the president "felt compelled by the need to ensure justice to the victims, especially in view of the nature of the crimes [Abdullah Shah] committed".