The looters broke into the new 'Nicola Amici' high school in Acquasanta Terme, one of the towns in the Marche region which was badly damaged in the earthquake of August 24th. The robbery took place on Tuesday night.
Six of the computers had been provided by the Italian Ministry for Education, while the remaining four were donations which had only arrived the previous day.
"I am outraged by this act of horrendous looting," said mayor Sante Stangoni, according to La Repubblica.
"We are working hard to keep the town alive, we are putting in maximum effort every day. There are some people who don't respect anything, not even the pain and tragedy we are going through."
The school was set up at the start of the new term because the two existing schools in the town were no longer usable due to quake damage.
Overall, almost a third of the schools in the affected area (28 percent) are unfit for use following the disaster.
Education Minister Stefania Giannini said the ministry would ensure the schoolchildren had new computers to work on as soon as possible, while tax collection agency Equitalia also said on Twitter that it would help provide the school with computers.
The Italian Chamber of Deputies has pledged to use the money saved from its budget this year (€47 million) to help with the recovery of the damaged towns.