"Several hooded youths" ambushed the firefightrers and police officer on Thursday night, officials said in a statement.
On Friday afternoon around 150 people gathered in front of the Ajaccio police headquarters in a show of support for the victims.
A breakaway group formed and targeted the prayer hall near the housing estate, shouting "Arabs get out!" or "This is our home!" in the Corsican language.
They trashed the hall and tried to set fire to copies of the Koran, with only partial success.
Some 50 prayer books were thrown into the street with some of the pages burnt, according to regional official François Lalanne.
French Prime Minister Manuel Valls wrote on Twitter that the break-in was "an unacceptable desecration", also condemning the "intolerable attack" on the firefighters and police officer.
Corsican nationalist leaders, who this month won control of the regional council, condemned both incidents, slamming "racist acts completely contrary to the Corsica that we want to see", in the words of regional executive chairman Gilles Simeoni.
Dalil Boubakeur, the rector of the Grand Mosque of Paris, said he was "dismayed and saddened" by the events in an appearance on France's BFMTV, calling on people to keep "calm and cool heads".
Lalanne said that police would remain present on the housing estate and would receive reinforcements in the coming days.
Local officials, including Prefect Christophe Mirmand, vowed to arrest those responsible.
French Interior Minister Bernard Cazeneuve said the attack on the 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".
The Christmas violence came amid heightened security measures for the season in France after the 13 November attacks by jihadists in Paris that killed 130 people.