Sabeen Mehmud was shot dead in Karachi as she drove home with her mother, who was injured in the attack.
A statement from Mr Sharif's office expressed condolences and ordered an immediate investigation.
No group has yet said it carried out the killing; the campaigner been subject to death threats before.
"It's an incident of targeted killing," said Dr Jamil Ahmed, the Karachi-South Deputy Inspector General of Police, who said it was too early to establish a motive, Dawn newspaper reported.
Her killing came hours after she hosted a talk on the Pakistani army's alleged involvement in the torture and killing of political activists in restive Balochistan province.
The talk was originally due to be held earlier this month at a university in Lahore but authorities cancelled it.
Ms Mehmud, 38, was a director of the charity The Second Floor, also known as T2F.
T2F regularly holds seminars on human rights issues. It houses a cafe and book shop where Karachi's liberal activists and students can meet.
When you don't see that many people stand up, and you do, you are very likely to stand out. Sabeen knew that and went ahead and did it anyway.
It's a huge thing when you have been told to call off an event, only to go ahead and do the same event in a public space, when it's so dangerous in Pakistan.
It is difficult to believe someone so vibrant, so alive, so determined is gone. There is a disbelief in Pakistan, on social media and from young people.
Ms Mehmud set up T2F having already established a charity, PeaceNiche, in Karachi. She said she "maxed out seven credit cards" to keep the centre going.
She also helped promote the importance of learning computer skills among Pakistani youth, and hosted hundreds of events at T2F.
In a profile in a Pakistani media magazine in 2013, Ms Mehmud was asked what her superpower would be. She answered: "I'd like to wave my magic wand and de-weaponise Karachi."
Pakistan's Prime Minister, Nawaz Sharif, has led condemnation of the killing of leading human rights activist Sabeen Mehmud.