The attack was the latest in a five-year insurgency which has claimed the lives of nearly 3,700 people.
The region bordering Malaysia was an independent Malay Muslim sultanate until annexed by Thailand a century ago.
The ICG study was compiled over 16 months and its release comes amid the latest escalation of violence that has left at least 36 people dead and more than 60 wounded in the past two weeks.
According to Rungrawee Chalermsripinyorat, the ICG's Thailand analyst, recruiters appeal to a sense of Malay nationalism and pride in the old sultanate.
"They tell students in these schools that it is the duty of every Muslim to take back their land from the Buddhist infidels," Rungrawee told the Associated Press.
Muslims make up more than 90 per cent of the two million people in southern provinces of Yala, Pattani, Narathiwat and Songkhla.
Many complain of being treated as second-class citizens in mainly Buddhist Thailand.
The area was a semi-autonomous Islamic Malay sultanate until annexed by Thailand in 1902.
Several violent uprisings have been put down by the army over the century.
The latest uprising flared in January 2004 when fighters raided an army base, killing four soldiers.
Despite martial law imposed in 2004 and thousands of Thai troops in the region, frequent attacks blamed on Muslim fighters have left more than 3,700 people dead.
The report describes the classroom as "the point of first contact'' for recruiters who invite Muslim youths to join extracurricular indoctrination programmes in mosques or disguised as football training.
"Schools are particularly important as recruiting grounds because they have been the battleground for the clash of cultures and ideologies fuelling the conflict," the report said.
"Many Malay Muslims view state schools as a vehicle to inculcate 'Thai-ness,' while the government sees Islamic schools as a tool for Malay nationalist indoctrination."
Public school teachers are viewed by the fighters as symbols of Thai government authority and are regularly attacked.
Over the past five years, at least 115 public school teachers and education officials have been killed in the south, the US-based Human Rights Watch said last week.
The ICG report also said the primary aim of the movement was to protect the identity of the region's ethnic Malay Muslims.
The highly secretive fighters in Thailand's southern provinces have not specifically stated the motives behind their attacks, but they are also thought to be fighting to establish an independent state in the three Muslim-majority provinces.
The ICG also said the government's reluctance to work towards a solution "at the local level" was exacerbating the problem and it should avoid "quick fixes to what is a highly complex conflict".
"Changing these policies is essential as the government tries to respond to the insurgents' grievances in order to bring long-lasting peace to the region," ICG said.
Abhisit Vejjajiva, the Thai prime minister, has said his government sees education as a "key area" in dealing with the Muslim separatist movement in the south of the country, and that his government is trying to "turn things around".
In April, the Thai government announced it was extending emergency rule for another three months in the region, despite a promise in January by Abhisit to cancel the measure.