Muhammad Hussain was sentenced by a military court to death in 2009 for killing his senior officer Havaldar Khadim Hussain when they were on leave the year before, a report by Pakistan Today said.
The execution has been criticized by several human rights groups and condemned by France.
The newspaper said an official at the jail in Mianwali city in Punjab province confirmed Hussain was hanged this week.
The last execution before Hussain's was that of another soldier, Shahid Abbas, in December 2008.
Pakistani President Asif Ali Zardari placed an unofficial moratorium on executions soon after he was elected in 2008, Pakistan Today said.
Until now, Zardari has issued a letter every three months staying all executions.
Zaman Khan, an official at the Human Rights Commission of Pakistan, criticized the execution, saying it indicates the government has changed its policy, Pakistan Today reported.
The BBC reported that the chairman of the HRCP, Zohra Yusuf, told the BBC that she was "worried" by the execution and its timing.
"Only recently the president asked the government to work on a draft law to abolish the death penalty," the BBC quoted Yusuf as saying. "I hope this doesn't have implications for other cases. But I'm worried about what happens after March when this government finishes its term."
In October 2010, HRCP issued a statement calling upon the government to take "early and meaningful steps toward abolition of the death penalty as well as immediately make the informal moratorium on executions formal."
At the time the HRCP said it "joins the World Coalition against the Death Penalty and human rights organizations across the globe in observing Oct. 10 as World Day against the Death Penalty."
Amnesty International also said this week it is concerned about what the execution means for Pakistan.
"In the context of such rare progress on human rights in Pakistan, this execution is even more disheartening," Polly Truscott, deputy director of Amnesty International's Asia-Pacific Program, said.
Truscott said government officials claimed the execution was an exception to the rule of staying executions because the case was a military one.
"But the death penalty is no less offensive to human dignity and the right to life just because the person to be killed happens to be a soldier," Truscott said.
Amnesty, which said more than 8,300 people remain on death row in Pakistan, wants the government to establish an official moratorium on executions with a view to abolishing the death penalty, in line with U.N. General Assembly resolutions adopted since 2007.
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