The girl was killed when the blast went off around 7:45 am (0545 GMT) as the students were arriving in the yard in front of the Francesca Morvillo Falcone vocational school.
Local emergency official Fabiano Amati said that “two other pupils are in a critical condition”, including one who is “fighting for her life and undergoing surgery.”
“The first people to come to the aid of the injured were a teacher, a monitor and a technician (who) described a powerful explosion that knocked several students to the ground,” the school’s director Valeria Vitale told the daily newspaper La Repubblica. “The students are in shock.”
The injured are suffering from burns of different degrees of severity, media reports said.
Doctors were said to be fairly optimistic for the hopes of the girl who was operated on, whose sister was also injured, according to the website of La Repubblica.
Italian president Giorgio Napolitano said he was following developments “with apprehension” and reached out to the families of the dead student and the wounded.
Most Italian students have classes on Saturday morning, and other Brindisi schools sent their students home.
First indications from security forces said the bomb had been placed in a container near the school, but La Repubblica said the devices had apparently been left in backpacks in front of the school.
Italian media noted that the school is named after the wife of the famous anti-Mafia judge Giovanni Falcone.
The judge, his wife and their three bodyguards were killed nearly exactly 20 years ago on May 23, 1992, when the Sicilian Mafia planted half a tonne of dynamite on the road between Palermo’s airport and the city centre.