Windows were broken and the door damaged at the Audencia school in Nantes, run by 57-year-old Aissa Dermouche - the Algerian-born director of the management school and the new top administrator for the eastern French department of Jura.
Dermouche immediately went to the scene and a probe has been launched.
The explosive device used in the blast was "not very sophisticated", a source close to the probe said.
Last week, the car belonging to Dermouche was destroyed by an explosive device.
Dermouche, who came to France at the age of 18, is the first departmental governor, or prefect, from the generation that immigrated from North Africa in the 1960s.
The handful of previous Muslim prefects started their civil service careers before 1962 when Algeria was still a part of France.
The attack on Dermouche's (R)
car was widely condemned
His nomination 10 days ago came at a time of growing concern over how to integrate the five million-strong Muslim community in France amid moves by the government to ban Islamic headscarves and other religious insignia in schools.
Last Sunday's attack on Dermouche's car provoked condemnation from across the political spectum, amid fears it was a symptom of increasing tensions with the Muslim community.
No one was hurt in that attack, which took place before dawn.
Police have been looking into the possibility that the attack on Dermouche's car was the result of a private grudge rather than an act of Islamist or far-right terrorism, but no motive has been ruled out.