Noor Mukadam, 27, the daughter of former Pakistani ambassador to South Korea Shaukat Ali Mukadam, was found shot dead in Islamabad, police said on Tuesday.
Mukadam had not been in contact with her father since Monday morning.
According to unverified early reports, she had left home and was with the son of a well-known businessman.
The police in Islamabad said the man, Zahir Jaffer, was a US citizen and had booked a flight to the United States on Wednesday.
They said this may be evidence of premeditated murder and an attempted flight from justice.
Zahid Hafeez Chaudhri, the spokesman for Pakistan’s Ministry of Foreign Affairs, expressed his condolences to Mr Mukadam on Twitter, with the hashtag #JusticeForNoor.