Initial results from trials in 2,260 adolescents in the US also suggest the vaccine is safe with no unusual side-effects.
The drug company says it will submit its data to the US and European authorities for emergency use in 12- to 15-year-olds.
There are currently no plans for children to be vaccinated in the UK.
Children's risk of becoming very ill or even dying with Covid-19 is tiny, and throughout the pandemic they have very rarely needed hospital treatment.
Adults - particularly those over 50 and people with serious underlying health conditions - have a much higher risk, which is why they have been vaccinated as a priority in the UK.
Pfizer is one of a number of drug companies testing their Covid vaccines on children. The aim of vaccinating them - particularly older children - would be to keep schools open, reduce the spread of coronavirus in the community and protect vulnerable children with conditions which put them at increased risk.
AstraZeneca announced trials of its vaccine in UK children aged six to 17 some time ago, and the first of 300 volunteers were due to be jabbed last month. The vaccine is currently only authorised for people aged 18 and over in the UK.
Alongside trials in teenagers, the Pfizer-BioNTech vaccine, which is authorised for use in those aged over 16, is also being tested in children under 12, with the aim of involving babies from just six months old.
The company started dosing the first healthy, young children in this trial last week.
In the Pfizer trial in 12- to 15-year-olds, 18 cases of Covid-19 were seen in the group given a dummy vaccine and none in group given the Covid vaccine which protects against it.
All participants received two doses 21 days apart, and the 18 cases were all children with symptoms. There were no tests for asymptomatic infection - children displaying no symptoms.
The figures are preliminary and full data has not been released, peer-reviewed or published in a journal.
Dr Peter English, former consultant in communicable disease control and past chair of the BMA public health medicine committee, said more detail was needed to properly evaluate the company's claims.
"It would be useful to know how effective the vaccine is at preventing asymptomatic infection. Young people are less likely to have severe disease; and when they are infected, they are more likely to have asymptomatic infection, allowing them to transmit the disease to others," he said.
The company's press release also doesn't mention the impact of variants on the trials, how cases were identified in children and whether a longer gap between doses was tested.
'Next school year'
Albert Bourla, chairman and chief executive officer of Pfizer, said the company was "encouraged" by the clinical trial data.
"We plan to submit these data to FDA [US Federal Drugs Administration] as a proposed amendment to our Emergency Use Authorization in the coming weeks, and to other regulators around the world, with the hope of starting to vaccinate this age group before the start of the next school year."
Ugur Sahin, CEO and co-founder of BioNTech, said the initial results in adolescents suggested children "are particularly well protected by vaccination".
He added: "It is very important to enable them to get back to everyday school life and to meet friends and family while protecting them and their loved ones."
Moderna, the US company behind another Covid vaccine ordered by the UK, has also started testing its jab on children under 11.