The new rules from the county Department of Public Health require anyone who has had close contact with a COVID-infected person to be tested before returning to campus. Previously, they could return if they were fully vaccinated and did not have any symptoms.
The health order, which applies to all public and private schools, also calls for masks to be worn in outside spaces where physical distancing is not possible.
Additionally, school staff will be required to wear a surgical grade or "upgraded" masks, as opposed to regular cloth ones.
A majority of the roughly 80 K-12 schools across the county resumed classes. The Los Angeles Unified School District, however, will return next week.
Students in the Burbank Unified School District were among those who returned to class Monday after the Board of Education decided not to delay reopening by one week.
The panel held a 3 1/2 hour emergency meeting Sunday night to consider the delay.
Superintendent Matt Hill announced the decision on the district's Facebook page. "After a robust discussion, the Board of Education decided that schools remain open."
District administrators will consider changes in its COVID safety plan this week including enforcing a vaccine booster requirement for all employees by April 1.
The district has 11 elementary schools, three middle schools, three high schools and five alternative schools.
Those who showed up for class Monday said they believe they felt safe returning.
"I do have some concerns about the COVID variant being around... but I hope that everybody will try and stay safe," said Burbank High School student Genesis Hopson.
City News Service contributed to this report.