According to CCTV footage, the girl in Kasur district was abducted last week outside her home.
"Tuesday night the girl's body was found from a heap of garbage in Saddar area of the city," Regional Police Officer (Kasur) Zulffiqar Hameed said, adding the body had been sent for autopsy.
"Initial autopsy report suggests that the girl was strangulated after rape," Hameed said.
The girl was staying with her relatives while her parents had gone to Saudi Arabia to perform Umrah, an Islamic pilgrimage to Mecca, Hijaz, Saudi Arabia, performed by Muslims that can be undertaken at any time of the year.
The police has taken four suspects into custody.
"We are trying to identify the person who was seen taking the girl along in the footage," he said.
Riots erupted in Kasur over police inaction after reports of the alleged rape and murder of the girl began circulating on social media.
The protesters pelted stone at the police station, offices of district police officer and district coordination officer in Kasur as the city observed a complete shutter down to protest against the brutal murder.
Widespread condemnation is pouring in from all mainstream leaders and national cricketers who are demanding immediate arrest of the culprits and exemplary punishment for them.
Police are resorting to 'direct' and aerial firing to disperse the protesters.
"Two persons who suffered serious bullet injuries during the protest succumbed to their injuries," a rescue official said.
Lahore High Court (LHC) Chief Justice Mansoor Ali Shah took notice of the murder of the girl and sought report from the Punjab government.
Punjab Chief Minister Shahbaz Sharif said he would personally monitor this case and would not rest till culprits brought to justice.
Ousted prime minister Nawaz Sharif has directed his younger brother Shahbaz Sharif to immediately arrest the culprits and bring them to justice.
Ruling PML-N member Punjab Assembly Hina Butt submitted a privilege motion in the assembly, seeking justice for 11 other minor girls who were killed after rape in Kasur and adjoining areas during the last year.
Opposition PPP chairman Bilawal Bhutto has termed the brutal rape and murder of the girl as "shocking and a slap on the face of Sharifdom (Sharif brothers)".
Test cricketers Shoaib Malik, Mohammad Hafeez and Wahab Riaz tweeted that it was unbelievable that this brutal incident took place in Pakistan. "Our thoughts are with the parents of the girl," they said and demanded immediate arrest of the culprits.