The accused, Kuldeep Singh, who was arrested from New Delhi, is the son of a retired Chandigarh Police sub-inspector.
The victims Manpreet Kaur and Rajwant Kaur were residents of Fazilka district in Punjab and were living in Chandigarh's Sector 22.
Senior Superintendent of Police Nilambari Jagdale told the media that Kuldeep Singh couldn't persuade Manpreet Kaur to change her decision to marry someone else. In a fit of rage he then strangulated her and slammed her body to the ground. He also stabbed her with a scissor.
Later, he killed her sister Rajwant Kaur, who was in the bathroom.
Jagdale said the accused and Manpreet Kaur knew each other for the past 8-10 years. Even their family members knew about their relationship.
"For the past six-seven months their relationship had soured and the girl was planning to get married to someone else. And prima facie the cause of the crime was jealousy and heartburn," she added.
According to the police, the accused has no criminal record.
This is the second heinous crime to have taken place in Chandigarh in less than a fortnight.
The blood-soaked bodies of an elderly couple were found under mysterious circumstances at their residence in Sector 40 on August 4.
( With inputs from IANS )