The ambush of the soldiers of the Afghan National Army reportedly occurred last Sunday in the province's Warduj district.
The New York Times said the province had been mostly quiet until recently as it is away from insurgent-held areas.
The Times quoted Abdul Marouf Rasikh, a spokesman for the provincial governor, as saying Wednesday a soldiers' convoy was ambushed and one soldier died and another 22 were captured.
He said tribal elders then went into negotiations and the insurgents released six of the soldiers, while the other 16 were executed by the insurgents and that the elders were given the bodies to be handed over the Afghan authorities.
The Wall Street Journal quoted a provincial police official that the released soldiers were exchanged for 10 Taliban prisoners.
The Journal quoted Rasikh as saying the governor's office had received reports some foreign fighters were also among the insurgents.
In a statement, Taliban spokesman Zabihullah Mujahid denied some of the soldiers taken captive were executed by insurgents. He claimed 15 of the troops were immediately killed in the initial fighting and that one of the prisoners later died of his wounds.
The Journal said the latest incident comes as U.S.-led NATO forces withdraw from the country. Afghan security forces are to take charge of security of their country after foreign forces end combat operations by the end of 2014.
The BBC said the attack in Badakhshan province, bordering Tajikistan, China and Pakistan, indicated growing Taliban activity in areas once regarded as being safer than others in the country. The report said the province with its mountains and valley, offers perfect cover for insurgents.
Dowlat Waziri, a spokesman for the Afghan Defense Ministry, said in the past 10 weeks, 97 Afghan National Army troops have been killed in combat, the Journal reported. The report said the numbers do not include significant losses among Afghanistan's police forces and intelligence service.