A video appearing to show the punishment has been posted online.
The 30-second clip shows a woman in a hole in the ground surrounded by turbaned men who hurl stones at her. Her fiance was lashed.
The woman, named as Rokhshana and aged between 19 and 21, can be heard repeatedly and desperately professing her Muslim faith as the stones strike.
The Tolo news agency reported that the killing took place about a week ago in a Taliban-controlled area just outside Firozkoh, the capital of central Ghor province.
It has been sourced and released by international broadcaster Radio Free Europe. It reported that a crowd of spectators captured the incident on their mobile phones as the woman's cries filled the air.
The woman and her 23-year-old fiance had allegedly fled from their families in a bid to find a place to be married, RFE reported.
Officials in Ghor told the AFP news agency that Rokhshana was stoned by a gathering of "Taliban, local religious leaders and armed warlords".
Provincial Governor Seema Joyenda - one of only two female governors in Afghanistan - said Rokhshana's family had arranged for her to be married against her will.
She was allegedly caught having pre-marital sex with her boyfriend - an act not tolerated by many conservative Muslims in rural Afghanistan.
"This is the first incident in this area [this year] but will not be the last," Ms Joyenda told AFP.
"Women in general have problems all over the country, but in Ghor even more conservative attitudes prevail."
Rokhshana's fiance was let off with only a lashing, Ms Joyenda said.
Mob killings are not uncommon in Afghanistan.
In March a woman called Farkhunda was savagely beaten and set ablaze in central Kabul after being falsely accused of burning a copy of the Koran.
The murder triggered protests across the country and led to global condemnation of the treatment of Afghan women.
A young woman has been stoned to death in central Afghanistan after being accused of adultery, officials say.