The Kirkcaldy and Cowdenbeath MP, who is now a UN special envoy, said he had spoken to the Pakistan High Commissioner in the UK shortly before 14-year-old Malala Yousafzei arrived in Birmingham for specialist care.
The girl, who was shot after speaking out about her suffering under the Tablian regime, is to undergo specialist care at the Queen Elizabeth Hospital in the city.
Mr Brown said he would visit Pakistan President Asif Ali Zardari and raise the issue of Malala's cause of education for girls.
He is also supporting an online petition to raise awareness of the 32 million girls in developing countries who are unable to go to school.
Mr Brown said: "As Malala fights for her life, a worldwide campaign continues to grow around her in support of her demand for education for every girl.
"In Pakistan, as well as India, Bangladesh and Afghanistan and along with the West, Malala's courage is inspiring revulsion against the Taliban.
"She is becoming for millions of children their adopted sister and for millions of parents their adopted daughter."
Malala was shot on a bus in front of her friends a week ago because she had criticised the regime for denying her the right to go to school.
Her life was saved by neuro-surgeons in a Pakistani military hospital and she has since been in intensive care.
However, doctors decided she needed "prolonged care" to help her recover from the physical and psychological effects of the attack.
Mr Brown added: "I know the Birmingham hospital where Malala is to be treated.
"I have visited patients, doctors and nurses there on a number of occasions and I have seen at first hand their expertise in dealing with injuries caused by gunshot wounds."
The former Labour leader, who represents the UN in the field of global education, said a Unesco survey had revealed 61 million children have, like Malala been denied the right to school. He added it was clear in many countries that "opportunity through education is still an empty promise".
Mr Brown said: "Their plight reveals the extent to which it is still birth and background –where you come from and who you were born to – that matters far more in deciding your prospects than your talent or merit.
"Altogether 32 million girls like Malala are excluded from school, many like her discriminated against because of their gender. Millions more are offered an inferior education to their male counterparts."
The petition will be handed to Mr Zardari and UN Secretary-General Ban Ki-moon, who has written to the child's parents.
Foreign Secretary William Hague praised Malala. He said: "Malala's bravery in standing up for the right of all young girls in Pakistan to an education is an example to us all.
"Malala will now receive specialist medical care in an NHS hospital. Our thoughts remain with Malala and her family at this difficult time.
"The public revulsion and condemnation of this cowardly attack shows that the people of Pakistan will not be beaten by terrorists.
"The UK stands shoulder to shoulder with Pakistan in its fight against terrorism."
Malala was shot with two classmates as they made their way home from school in Swat, in the north-west of Pakistan.