The violence came on Christmas day amid heightened security measures for the holiday, and nationwide fears after the November 13 attacks in Paris by jihadists that killed 130 people.
French Prime Minister Manuel Valls wrote on Twitter that the break-in in the city of Ajaccio was "an unacceptable desecration".
Tensions had mounted in Ajaccio Friday after two firefighters and a police officer were injured overnight in a low-income neighbourhood of the city when they were "ambushed" by "several hooded youths", authorities said.
On Friday afternoon around 150 people had gathered in front of the prefecture in a show of support for the police and firefighters, officials said in a statement.
But some in that crowd broke away and headed for the low-income housing estate where the violence took place the night before.
They shouted slogans in Corsican meaning "Arabs get out!" or "This is our home!", an AFP correspondent reported.
Nearby was the Muslim prayer room and a small group smashed the glass door and entered the place of worship, ransacking the room and partially burning books including copies of the Koran, said regional official Francois Lalanne.
"Fifty prayer books were thrown out on the street," Lalanne said, adding that some of the pages were burnt.
The French Council of the Muslim Faith (CFCM) and its monitor of Islamophobia denounced the violence and pointed to the timing of the attack on Friday "on a day of prayer for both Muslims and Christians".
This year Christmas falls just after the Muslim feast day commemorating the birth of the Prophet Mohammed.
French Interior Minister Bernard Cazeneuve said the attack on the Muslim prayer hall showed signs of "racism and xenophobia".
He also condemned the assault on law enforcement and safety officers in Corsica, saying he hoped "the authors of the violence would be identified and arrested as soon as possible."
Local authorities including Christophe Mirmand, the prefect or top official of Corsica, also vowed to arrest those responsible for the outbreak of violence over two days on the Mediterranean island.
Corsica is a department of France which held regional elections earlier this month, which had seen the far-right anti-immigrant Front National make unprecedented gains in the first round of the vote.
On Corsica the nationalists won the regional election there taking power for the first time.