Local police official Mohammad Ismail Hotak said the bodies of the couple -- whose names and ages weren't reported -- were found Tuesday in Lashkargah city. Police described the couple as "young."
The woman allegedly ran away from her home after the man promised to marry her, Hotak said.
The brother of the male victim said the couple were abducted by gunmen.
Affairs outside of marriage are considered a sin in Afghanistan and honor killings of women for such actions are not uncommon, Khaama Press reported.
In the past two years, nearly 400 honor killings and rape cases were recorded in Afghanistan, an independent human rights commission said.
2014: The Year in Music [PHOTOS]