Dr Albert Bourla said yearly vaccinations could boost population immunity, adding that the company is already working on a new jab for the Omicron variant.
He told the BBC: "Based on everything I have seen so far, I would say that annual vaccinations... are likely to be needed to maintain a very robust and very high level of protection."
It is not yet clear whether the vaccines will need to be tweaked every year for new variants, as happens with the annual flu jab.
In October, the United States Food and Drug Administration approved the Pfizer jab for five to 11-year-olds.
Dr Bourla said immunising that age group in the UK and Europe would be a very good idea.
"Covid in schools is thriving," he said.
"This is disturbing, significantly, the educational system, and there are kids that will have severe symptoms.
"So there is no doubt in my mind that the benefits, completely, are in favour of doing it."
Ministers in the UK have announced they have secured Covid-19 vaccines for potential booster campaigns in the next two years.
The Government there said it has signed deals for 114 million Moderna and Pfizer jabs, which will be delivered in 2022 and 2023.
UK Health Secretary Sajid Javid said the deals "future-proof" the country's vaccination programme.
They include 60 million additional doses of the Moderna vaccine and 54 million more Pfizer/BioNTech doses.
The Department of Health and Social Care said the deals include access to modified vaccines if they are needed to combat Omicron and future variants of concern.
It said the new deals are in addition to 35 million additional doses of Pfizer/BioNTech ordered in August for delivery in the second half of next year, and the 60 million Novavax and 7.5 million GSK/Sanofi doses expected in 2022.
The department said the Government already has enough supplies of both Moderna and Pfizer/BioNTech for the expanded booster programme.
It comes after officials announced that all adults in the UK will be offered a booster shot before the end of January amid growing concerns about the Omicron variant.
Vaccination experts advising the Government have expressed preference for the mRNA vaccines - Pfizer and Moderna.
Trial data suggests booster doses are generally well tolerated and provide a substantial increase in vaccine-induced immune responses, in particular, and that mRNA vaccines provide a strong booster effect.
Mr Javid said: "Thanks to the Vaccines Taskforce, we have an excellent track record of securing the vaccines the country needs to keep this virus at bay.
"These new deals will future-proof the Great British vaccination effort - which has so far delivered more than 115 million first, second and booster jabs across the UK - and will ensure we can protect even more people in the years ahead.
"This is a national mission, and our best weapon to deal with this virus and its variants is to get jabs in arms - so when you are called forward, get the jab and get boosted."
But the announcement came as global health leaders questioned booster campaigns.
Dr Mike Ryan, executive director of the World Health Organisation's health emergencies programme, said he is not aware of any evidence that would suggest offering booster jabs to the entire population gives any greater protection to healthy people.