All girls "and not just the sporty ones" should take physical exercise, Helen Fraser, chief executive of the Girls Day School Trust (GDST), said.
Research that girls are far less active than boys is worrying, she said.
"Girls who are in schools which focus solely on academic achievement can experience success after success, and may never learn that you can have a real setback and come back and recover", Fraser told BBC News.
Fraser said she backs "sport for all".
"That's why I love it when our schools have A, B ,C and D teams and beyond", she said.
The GDST draws on research from the Women's Sport and Fitness Foundation which suggests only a quarter of girls in England meet current recommended levels of physical activity each week, with the proportion taking part in regular sport falling steeply after the age of 10.
One in five girls do no physical activity at all, twice the proportion of boys, the research suggests.
She says similar high proportions of female executives believe sport made them more disciplined, resilient and competitive in their careers.
"I think sport and exercise are ways in which women can reclaim their bodies from the kind of obsessions of the tabloid press and celebrity magazines", says Fraser.
The GDST is composed of 24 fee-paying schools and two academies in the UK.
