They say the constant pressure by social media is taking a toll on teenagers' mental health.
Deputy headteacher Cindi Pride said: "There have been many reports about how excessive use of social media can have a negative impact on mental health, particularly for girls.
"And the situation is getting worse. It can have a real impact on self-esteem with people comparing themselves to others.
"We are also banning FitBits and smartwatches.
"These monitor the number of calories burned and we found that some girls would monitor the number of steps they had taken and the number of calories they had used.
"If they didn't feel they had taken enough steps in the morning they wouldn't eat lunch."
She added: "We don't need our girls to be counting calories.
"They are young women who are fit and healthy and they do exercise and PE and do not need to be obsessed with steps of calories."
The school - rated 'outstanding' by Ofsted - carried out a survey earlier this year which found 71 per cent of pupils admitted checking or responding to social media 'constantly.'
They ran a charity 'detox week' to raise cash to help teens with mental health problems.
When pupils return from their summer break, girls in Years 7 to Year 9 will be banned from using their mobile phones at all during the school day.
Older girls in Years 10 and 11 will be allowed to use their mobiles at lunch, and pupils in the sixth form - which includes boys - will be allowed to use their phones freely except in lessons.
In a letter to parents, assistant headteacher Nadine Moore said 'Fear of Missing Out' was an additional pressure faced by teens through social media.
She wrote: "Being a teenager is hard enough, but the pressures faced by young people online are unique to this digital generation.
"Research suggests that young people who are heavy users of social media - spending more than two hours per day on social networking sites are more likely to report poor mental health.
"Seeing friends constantly 'having fun' can make young people feel like they are missing out while others enjoy life.
"Whilst for many young people Fear of Missing Out (FOMO) may not be a problem, for others it is causing them distress in the form of anxiety and feelings of inadequacy."
One parent said: "This is a good move, which addresses important issues in an appropriate and measured way.
"Hopefully it will mean that the students communicate with each other more on a face-to-face basis in the real world."
