The incident took place in Chak Sardarpur where Mumtaz Mai was asleep in her home with her children, when unknown men threw acid on them.
They were severely burnt and were taken to Civil Hospital by area residents where they were provided first aid facilities.
However, Mumtaz and her 14-year old daughter Saba had to be shifted to Nishtar Hospital in Multan in critical condition.
The reasons for the attack are still unknown and no arrests have been made but Police have started investigations.
Acid attacks are one the most common form of violence against women in Pakistan. These are various reasons behind the assaults which includes personal reasons as marriage proposal rejections or divorce issues, property and land disputes and also due to religious extremism.
There are an estimated 80-100 cases of acid attacks in Pakistan every year although independent organizations consider the figure to be much higher.
The Protection of Women against Violence Bill 2015, was passed in Punjab on February 24, which criminalizes all forms of violence against women, including domestic, sexual, psychological, emotional, economic and verbal.
The provincial government will establish district protection centers, residential shelters and a toll-free helpline for victims of violence under the law.
It also states that family courts must hold hearings within seven days of a complaint being made, and a decision must be taken on all complaints within 90 days. For serious offences, courts can order for a decision.