A boy aged 16 and a 27-year-old woman were also injured after the substance, believed to be acidic, was thrown at the victims outside Westminster Academy on Monday afternoon.
Police believe the teenagers were approached by a lone suspect who was on an e-scooter, with a member of staff left injured after she rushed to help.
Police were still hunting the suspect on Wednesday.
Corey McFaralane, the father of the 14-year-old pupil, told The Standard his daughter was in a stable condition after sustaining burns to the left side of her face, but could be scarred for life.
The 37-year-old from Westminster said: “She’s very traumatised by the attack.
“She’s very scared about her injuries. She’s a young girl, and these scars could be for life. She’s very worried about that and has been asking about that.”
Mr McFarlane said he has been staying at his daughter’s bedside in hospital, waking every couple of hours to administer eye drops and apply paraffin to her face “to keep everything in place”.
He said: “I can’t explain what I’m going through. Words can’t explain it.”
He added that the family “haven’t got any idea” of the motive behind the attack.
His older daughter, aged 16, has been at home since the attack and no longer feels safe going out to school.
Mr McFarlane has also set up a GoFundMe for his daughter which aims to raise £9,000.
According to the donation page, the funds would “help cover her expenses and support her journey to recovery”.
In a message posted on the site, Mr McFarlane said: “Words cannot express the shock, pain, and trauma she is going through right now, both physically and emotionally. This senseless act of violence has left her with severe injuries that require urgent and long-term medical care, surgeries, rehabilitation, and mental health support.
“We are humbly asking for donations to help cover her expenses and support her journey to recovery. Any contribution, big or small, will make a huge difference in her life and help us take the first steps towards healing from this unimaginable attack.”
Both teenage victims remain in hospital, with the boy’s injuries described as not life-threatening or life-changing.
The 27-year-old woman has since been discharged.
Scotland Yard said two officers were also taken to hospital as a precaution after they reported feeling unwell.
Detective Chief Inspector Dean Purvis, who is leading the investigation, previously said: “From our inquiries so far we believe the two young victims were on Alfred Road when they were approached by a lone suspect who threw a substance at them before fleeing down Harrow Road.
“A member of staff bravely and selflessly rushed to provide first aid to the two victims, sustaining injuries to herself in the process. Fortunately she has now left hospital.
“For the 14-year-old girl we might not know for some time how severe her injuries are but at this time they are being treated as life-changing.
“I know how incredibly concerning this incident is to parents and pupils and the wider Westminster community. We are in close contact with the school and local authority, and I can assure people that a thorough investigation is well under way, and that my officers will not stop until the suspect is found and arrested.
“If you have information that can help us, it is imperative that you tell us immediately. The area at the time was busy with people and cars. I am particularly interested in hearing from anyone who might have captured dashcam footage that can help us establish what happened.”
The suspect is described as a tall, slim, black male, wearing dark clothing with his face obscured, possibly by a mask or balaclava. He rode an e-scooter to and from the scene.
Westminster Academy’s principal, Numera Anwar, said in a statement: “One pupil, a teacher and a member of the public have been injured in an incident outside the school building on the main road involving an acid-like corrosive substance.
“This was a distressing incident which took place after school hours when students and staff were leaving the school site.
“We are offering support to families and relatives of all involved.
“This is a difficult time for our community and I took the decision to close the school (on Tuesday) to allow for a thorough investigation and to ensure the school can resume normally from tomorrow with all safety measures in place.”
Adam Hug, leader of Westminster City Council, added: “This is a truly shocking attack on school pupils and a member of staff.
“The council has been in touch with Westminster Academy and we will provide educational psychologists and any other support to help children through what is a traumatic ordeal. Our thoughts are with all those who have been affected.
“Clearly this attack will be unsettling for the whole academy and the wider community, and we will be working with police to provide reassurance and whatever support we can. We would urge anyone with information about what has happened to contact the police.”
Any witnesses or anyone with information is asked to call police on 101, quoting reference CAD 4987/30 Sept, or call Crimestoppers anonymously on 0800 555 111.