"The paper's done," Woollard told the Record Searchlight newspaper of Redding. "There is not going to be a school newspaper next year."
The school newspaper also ran in its June 3 edition an editorial written by editor-in-chief Connor Kennedy that defended flag burning as speech protected by the First Amendment.
Kennedy graduated last week from the high school in Redding, about 160 miles north of the state capital. He told The Associated Press he chose the topic because he had just studied flag burning in a class on government.
"I'm deeply saddened, and I find it terribly ironic a high school newspaper would be shut down for exercising free speech — particularly when the curriculum being taught was that this was free speech," Kennedy said in a phone interview Tuesday.
A press-freedom advocate said the student journalists were within their legal rights to publish the photo and editorial.
"I don't think any newspaper should ever be discontinued as punishment for things students have written, especially when what they've written about is the defense of free speech and what they have said is absolutely correct," said Terry Francke, general counsel of the nonprofit Californians Aware, which advocates for First Amendment issues.
Nevertheless, state law does not require schools to spend money on student newspapers or elective journalism classes, Francke said.
The school principal said eliminating the paper had been an option before it published the flag photo because the school expects to get less state funding next year and needs to save money.
The students' decision to showcase flag burning "cements the decision" to pull funding from the newspaper, he said.
The newspaper's cover was a collage of photographs, some of which showed students in what appeared to be prom attire. Prominently displayed at the top of the collage was a photograph of a student holding a flag pole, with the American flag burning at its edge.
Woollard did not respond to a telephone call Tuesday from The Associated Press.
The Redding controversy is the latest example in recent years of high school and college administrators in California attempting to censure student-run newspapers or punish those who oversee them.
In Los Angeles, a high school newspaper adviser was removed after he refused to withdraw a November 2006 student editorial criticizing random searches on campus. In 2003, Novato journalism teacher Ronnie Campagna was similarly replaced when the student paper published stories critical of San Marin High School.