A 13-year-old Brisbane schoolboy has been remanded in custody over the stabbing death of a fellow student.

The case against of the boy, who cannot be named, was briefly mentioned in Brisbane Children's Court today.

Twelve-year-old Elliot Fletcher died after the incident in the schoolgrounds of affluent St Patrick's College, Shorncliffe, yesterday morning.

The 13-year-old boy's lawyers made no application for bail and he was remanded in custody to reappear in court on April 29.

The boy did not appear in court and no details of charges were read.

Police said the boy had been charged with one count of murder.

Last night, police removed violent and pornographic postings from online tribute pages set up for Fletcher.

Police said they had moved to erase the offensive content from Facebook overnight, adding that those responsible for the posts could be traced and prosecuted.

Tribute pages popped up on social networking sites after the tragedy.

St Patrick's College is a waterfront Catholic day school in Shorncliffe, about 16km north of central Brisbane.

Australia has been shaken by the stabbing at the private boys' school, the second incident at a Brisbane school in a fortnight.

Two weeks ago a 16-year-old Catholic student at St Joseph's College in central Brisbane was stabbed in the leg, allegedly by a teenager from another school, who has been charged with the assault.

Queensland Premier Anna Bligh yesterday ordered a review of school security, and said her heart went out to Elliot Fletcher's family and the school community.

"I think it's fair to say that schools in Queensland are not like some of the schools we might see in some of the big cities in the United States. We don't have a serious problem with children bringing implements and weapons to school."

She added: "We'll be certainly looking at the arrangements of school security [and] if there are any lessons that will protect other students, of course we will look at them."

Few details of what was apparently a fight between two boys were available yesterday.

Police said preliminary investigations indicated two St Patrick's boys had been involved in an altercation at the school about 8.15am.

"During the altercation a 12-year-old boy sustained critical injuries and was transported to the Royal Children's Hospital, where he passed away," the police statement said.

"A 13-year-old boy was located a short time later in the nearby vicinity with a minor wound which required hospital treatment."

St Patrick's headmaster Michael Carroll did not comment beyond a brief statement.

"This has been a tragic loss of young life," he said. "My immediate concern is the welfare of the families affected and all students and staff."

Outside the school, a mother who did not want to be named told AAP she had been in tears.

"The first thing you think of is, is it my son?" she said. "To think that something so awful could happen. They're just little boys. It's very upsetting."

St Patrick's - motto "fight the good fight" - was established in 1952 by the Christian Brothers and has about 1000 students.

- AAP, additional reporting by Greg Ansley