Officials say a small group of protesters also tried to burn copies of the Koran in the capital, Ajaccio.
Overall, several hundred people gathered in the city to express support for two firefighters and a police officer injured on Thursday.
The government condemned both acts, pledging to punish the perpetrators.
On Friday, the crowd gathered in front of the prefecture in Ajaccio to show their solidarity with the firefighters.
Some protesters later marched to the scene of the attack on Thursday night - a poor neighbourhood in the capital.
They chanted "Arabs get out!" and "This is our home!", AFP news agency reports.
The demonstrators then attacked the local Muslim prayer room, ransacking it and partially burning books - including copies of the Koran.
French Prime Minister Manuel Valls said the attack was "an unacceptable desecration".
The French Council of the Muslim Faith also denounced the violence.
In Thursday's incident, the firefighters were ambushed by "several hooded youths", French media report.
Interior Minister Bernard Cazeneuve pledged that the perpetrators of both the attack on the emergency services and the Muslim prayer hall would be identified and arrested.
Mr Cazeneuve also stressed that there was no place for "racism and xenophobia" in France.
France has beefed up security measures for the Christmas holidays, following the 13 November attacks in Paris by Islamic militants that left 130 people dead.
A crowd has vandalised a Muslim prayer hall in Corsica in apparent retaliation for an attack on firefighters in the French Mediterranean island.