They say it is one of the first such cases of its kind in the region.
Honour killings happen when mostly male family members believe the victim has brought dishonour to their community.
The Human Rights Commission of Pakistan reported 943 women were killed in honour killings last year.
That represented an increase of more than 100 from 2010.
But such happenings are rare in parts of Kashmir under the control of Pakistan.
Police say that the incident took place in a remote village in the southern district of Kotli. They say that the case was brought to their attention by the couple's eldest daughter.
It will not be clear until Friday - when the parents are due in court - if they admit or deny murder charges.
Local police officer Raja Tahir Ayub told the BBC that the girl's father became enraged when he saw his daughter "looking at two boys" riding on a motorcycle outside their home on Monday.