The couple were brutally killed by the woman's father and brother with meat cleavers after the family invited the 22- year-old man to their house in Nazimabad area.
"Initial investigations show that the gruesome killings were carried out by the Kulsoom Bibi's father and brother in the name of honour at their home after they invited Sajid, who was having an affair with her, to their house," Superintendent of Police Gulberg Bashir Ahmed Brohi said.
The accused as well as the rest of the woman's family members escaped from the house after the killings.
Honour killings are a major menace in the rural areas of Pakistan's four provinces of Sindh, Punjab, Baluchistan and Khyber Pakhtunkhawa but it is rare to see such killings carried out in a metropolitan city like Karachi.
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A joint session of the Parliament last year in October unanimously approved anti-honour killing and anti-rape bills.
The legislation on honour killings introduced strict punishment for the convicts making it tougher than the ordinary murder cases with those involved in honour killings in the name of family honour having to serve a mandatory prison sentences of 25 years.