"Parents do not have a constitutional right to home school their children," Justice H. Walter Croskey wrote in a Feb. 28 opinion for the 2nd District Court of Appeals.
Noncompliance could lead to criminal complaints against the parents, Croskey said.
An estimated 166,000 students in California are home schooled, but it was unclear how many of them are taught solely by an uncredentialed parent.
To earn a five-year preliminary teaching credential in California, a person must obtain a bachelor's degree from an accredited college or university and complete multiple examinations.
Until now, California allowed home schooling if parents filed paperwork to establish themselves as small, private schools; hired a credentialed tutor; or enrolled their child in an independent study program run by an established school while teaching the child at home.
The state left enforcement up to local school districts, but there has been little oversight.
The old system "works so well, I don't see any reason to change it," said J. Michael Smith, president of the Virginia-based Home School Legal Defense Association.
The ruling stems from a case involving Phillip and Mary Long, a Los Angeles-area couple whose eight children are enrolled or have been enrolled in Sunland Christian School in suburban Sylmar and occasionally have taken tests there.
But the children were educated at home by their mother, who does not have a teaching credential.
Attorneys for the state Department of Education were reviewing the ruling, and home schooling organizations were lining up against it.
Phillip Long vowed to appeal to the state Supreme Court.
"I have sincerely held religious beliefs," he said. "Public schools conflict with that. I have to go with what my conscience requires me."