Farzana Iqbal, 25, was fatally attacked on Tuesday because she had married the man she loved.
Mr Sharif had taken notice of the "brutal killing" in the presence of police, his press office said in a statement, adding that a "totally unacceptable" crime had to be dealt with promptly by law. "I am directing the chief minister to take immediate action and a report must be submitted by this evening to my office," it said, quoting Mr Sharif.
Mrs Iqbal's husband said police did nothing during the 15 minutes of violence outside Lahore High Court.
"I begged them to help us but they said 'This is not our duty'," said Muhammed Iqbal. "I took off my shirt [to be humble] and begged them to save her."
In parts of Pakistan, a largely Muslim nation of 180 million people, women are expected to agree to arranged marriages and refusal can mean an "honour killing".
Many Pakistani families think it dishonourable for a woman to fall in love and choose her own husband.
Lahore police chief Shafiq Ahmad insisted no police had been present during the killing. "They arrested the father, the main accused, a few moments after the incident," he said. "By the time police reached the scene, the lady had been murdered."
Police initially said Mrs Iqbal had been stoned, but her husband said relatives had swung bricks, not thrown them.
All of the suspects except the father have disappeared.
The 25-year-old had offended her family by marrying Mr Iqbal instead of a cousin selected for her.
Honour killings are common in Pakistan, but the brutality of this case caused outrage around the world.
In Pakistan the reaction was more muted - in stark contrast to the public grief and outrage caused by the gang rape and murder of a 23-year-old woman in neighbouring India in 2012.