Few details were available and the official said more than one device may have been involved in the explosion, which occurred as pupils were preparing to enter the school at the start of the school day, which in Italy includes Saturdays.
"Given the effect of the explosion, it appears that this was something quite powerful," the official said.
Local media reported that the device had been placed in a rubbish container just outside the school, which they said was near the main court in Brindisi, a port city located in Apulia, on the "heel" of Italy.
There was no claim of responsibility and no indication of who had placed the bomb.
Interior Minister Anna Maria Cancellieri announced plans several days ago to step up security around sensitive targets including official buildings after a series of threats against tax officials.
Italy's main tax and fine collection agency, Equitalia, has been targeted by a series of small explosive devices amid a growing wave of public anger over the high taxes imposed to shore up public finances and combat the economic crisis.
The head of Ansaldo Nucleare, a nuclear engineering company owned by defence technology group Finmeccanica, was shot in the leg in an attack claimed by an anarchist group, adding to concerns that extremist groups may try to exploit the public anger.