Police later arrested Mehmood and his son Abuzar when they confessed to killing Aneeqa by beating her to death.
They also admitted dumping her body as well as filing a false missing persons report.
A judge at a court in Lahore then awarded Mehmood the death penalty and also fined him 500,000 Pakistan rupees.
The case comes just a week after another man who murdered his daughter and her boyfriend in a so-called honour killing was allowed to go free after he pardoned himself and his accomplices.
Faqeer Muhammad was accused of shooting dead his daughter Kiran Bibi and her alleged lover Ghulam Abbas, "to save family honour" due to their relationship in Lahore in 2014.
Muhammad and the daughter's mother Azmat Bibi were the legal heirs to the girl, meaning they could pardon anyone accused of killing her.
Mrs Bibi and another son then lodged an application to have Muhammad pardoned, which he agreed to and it was accepted by the court.