According to the local officials, the incident took place in the remote and restive district of Wardoj.
The district administrative chief Dawlat Mohammad Khawar confirmed the incident and said the woman was stoned to death after she faced a trial openly along with the man from the Taliban insurgents.
This is not the first time the Taliban insurgents have public tried and executed women over adultery and other charges in Badakhshan.
According to the statistics provided by the local officials, the group has executed at least five women over various charges in the past two years in this province.
The Taliban insurgents executed at least two women including a pregnant woman and a girl in this province last month.
One of the victims was shot dead by the insurgents after she rejected a marriage proposal from one of their commanders while the other woman was killed after she had left the house of her in laws.
Badakshan is among the relatively volatile provinces in northeastern Afghanistan which has witnessed growing violence, mainly due to Taliban-led insurgency during the recent years.