Around 50 pupils in the town of Satkhira took to the streets to demand that Habiba Sultana's wedding be called off, they say.
Pupils even submitted a petition to police urging them to take action.
Police summoned Habiba's father and ordered him to stop the girl's marriage, which they said was illegal.
Her father was told to sign a bond in which he promised not marry off his daughter while she is still a child, the Bangladesh Daily Star reported.
It said that the wedding was to have taken place in the south-western town of Satkhira in Friday.
Police say that Habiba, a student of Abdul Karim Girls' High School, did not agree when her poverty-stricken father arranged for her to marry a 23-year-old neighbour.
Police say that she was too frightened to protest.
When she told her friends about the impending wedding, they rallied round and urged her not to go ahead.
Parents of her friends contacted Habiba's father and tried to stop him from going ahead with the wedding.
Initially he ignored their protests, but changed his mind after the police were alerted and small protests were held outside the school.
Correspondents say that the stand of the schoolgirls has created a stir in the town.
Like many other parts of the country - young people in Satkhira are deferential to their parents and seldom question their commands.