The study says girls as young as 10 are forced to marry much older men in countries including Afghanistan, Yemen, India and Somalia.
Save the Children says early marriage can trigger a cycle of disadvantage across every part of a girl's life.
Conflict, poverty and humanitarian crises are seen as major factors that leave girls exposed to child marriage.
"Child marriage starts a cycle of disadvantage that denies girls the most basic rights to learn, develop and be children," said Save the Children International CEO Helle Thorning-Schmidt.
"Girls who marry too early often can't attend school, and are more likely to face domestic violence, abuse and rape. They fall pregnant and are exposed to STIs (sexually transmitted infections) including HIV."
The report, called Every Last Girl, ranks countries based on the hardest place to be a girl based on schooling, child marriage, teen pregnancy, maternal deaths and the number of women in parliament.
Chad, Niger, Central African Republic, Mali and Somalia were ranked at the bottom of the index.
The report says girls affected by conflict are more likely to become child brides.
It says many refugee families marry off their daughters as a way to protect them against poverty or sexual exploitation.
The charity used the example of a 13-year-old Syrian refugee in Lebanon it called Sahar - not her real name - who was married to a 20-year-old man. Now 14, she is two months pregnant.
"The wedding day, I was imagining it would be a great day but it wasn't. It was all misery. It was full of sadness," Save the Children quoted her as saying.
"I feel really blessed that I am having a baby. But I am a child raising a child."
The report says girls also suffer during humanitarian crises such as the Ebola outbreak in Sierra Leone where the shutting down of schools led to an estimated 14,000 teen pregnancies.
The UN children's agency, Unicef, estimates that the number of women married in childhood will grow from 700 million today to around 950 million by 2030.
The Save the Children's report coincides with International Day of the Girl on Tuesday.