A total of 415 children aged 10 and under have been referred to the government's deradicalisation programme in England and Wales over the last four years, the BBC has learned.
National Police Chiefs' Council (NPCC) figures obtained by the BBC show 1,424 children aged 11-15 were also referred.
The "Channel" scheme, set up after the 7 July London bombings, aims to steer people away from extremism.
The government says the scheme has successfully deradicalised people.
The BBC obtained NPCC figures, under a Freedom of Information request, which showed that a total of 1,839 children aged 15 and under had been referred over concerns they were at risk of radicalisation between January 2012 and December 2015.
The figures show referrals are rising year on year.
The "Channel" programme, which is part of the government's counter-terrorism strategy, focuses on identifying people who are vulnerable to being drawn into terrorism and providing them with support to stop that from happening.
Those at risk of right-wing extremism can also be referred.
Sally Bates, of the National Association of Head Teachers' (NAHT) says it is important for teachers to be able to safeguard their pupils from extremism and radicalisation.
In some cases, young children had seen beheading videos with their families, she said.
"That does raise a number of concerns and that's where I can understand that referrals are then made from teachers."
Under laws brought in last summer, schools, prisons, the NHS, and local authorities have a legal obligation, known as the "Prevent Duty", to spot individuals who might be vulnerable to extremism and radicalisation.
Figures show most of the referrals in both age groups were made in November last year - after the new law came into force - suggesting it could partly be a reason for the increase in the number of referrals.
One parent, Ifhat Shaheen, told the BBC her 14-year-old son was interrogated by people working on the government's counter-terrorism strategy after he mentioned the word "eco-terrorists" in school.
He was taken aside at Central Foundation School in London and asked if he was affiliated to the Islamic State group, she said.
"A teacher's job is to teach children and not to spy on children," she said.
What is the 'Channel' programme?
"Channel" is the government's programme designed to stop vulnerable people from being drawn into violent and non-violent extremist or terrorist behaviour.
It is an "early intervention" scheme, designed to work with individuals of any age who are at risk of being exploited by extremist or terrorist ideologues.
The type of support is tailored to the individual, but may focus on a person's vulnerabilities around health, education, employment or housing, as well as specialist mentoring or faith guidance, or even broader diversionary activities such as sport.
Anyone can make a referral, including education, health, youth offending teams, police, social services, families or the community.
The programme is voluntary and, in the case of children, parental consent is needed.
Source: The Channel Programme
She added: "Schools are meant to be a safe place where you can have open dialogue and discussion."
"It's really heart-breaking to hear that young Muslim children are being criminalised in this way for the wrong reasons and an overreaction. It stigmatises Muslims."
Her son's school said the safeguarding and wellbeing of its young people was its main concern and it did not comment on individual cases.
At another school - Elizabeth Garrett Anderson School in north London - head teacher Jo Dibb said that no pupils had been referred to "Channel".
Part of the reason, she says, is that staff encourage conversation and debate about extremism rather than shying away from it.
"Just because a young person makes an off-the-cuff remark - it doesn't make them a terrorist.
"All young people will say things that they don't mean and it's our job as educators to make sure they understand what they're saying and that they can explore their ideas." If there was still concern, only then would a referral be made.
The Channel programme is voluntary and of the 4,000 referrals since 2012, only hundreds have agreed to take part.
Former teacher Khalsoom Bashir, from Muslim women's charity Inspire, says a rise in referrals shows more people have faith in the system.
The government says the "Channel" programme has changed lives - and pulled people away from a dangerous life of extremism.
Security Minister John Hayes said: "This is about safeguarding and it's working. This is about protection, this is about help, this is about providing all the support you need to make sure your children are safe."