Ifitkhar and Farzana Ahmed were taken from their home in Great Sankey, Cheshire, at sunrise, The Daily Telegraph reported. Their daughter, Shafilia, 17, disappeared in September 2003, five months before her body was discovered in Cumbria.
At a 2008 inquest, a coroner, Ian Smith, concluded the teenager had been the victim of a "vile murder." He said he did not believe she had run away from home.
The parents, who have denied any involvement in their daughter's death, were arrested in 2003 on suspicion of kidnapping. The charges were dropped because of lack of evidence.
The new arrest follows a burglary at their home by three men who bound Farzana Ahmed and four of her grown children. A daughter, Alisha, 22, has been charged with helping set up the home invasion.
Shafilia, who had run away from home twice before her final disappearance, had refused an arranged marriage in Pakistan. Her father later said he had come to terms with her decision.
But she left song lyrics suggesting a deep conflict between her parents' values and the life she wanted to live: "Desire to live is burning … But all they think about is honor."