The fire was reported shortly before 2 p.m. and was under control around 3 p.m., the Cambridge Fire Department said.
Though the cause of the fire is under investigation, Cambridge police spokesman Jeremy Warnick said the blaze was initially reported on the roof.
Assistant Fire Chief Gerard Mahoney estimated damages at between $2.5 million and $3 million. He said the roof was heavily damaged and the third floor suffered “significant” smoke and water damage.
The roof is made of a rubberized material, Mahoney said. “That stuff burns like gasoline when it gets going,” he said, saying it was a wind-driven fire.
The school, located at 100 Putnam Ave., was demolished last year, and construction of the new facilities, which will serve kindergarden through eighth grade, was to be completed by summer’s end. Mahoney said workers were not on the roof at the time of the fire.
“We are thankful that no one got hurt,” said Jeffrey Young, superintendent of Cambridge public schools.
Cambridge City Manager Richard Rossi said the city will assess damages at the school.