Los Angeles public schools are requiring students ages 12 and older to get the Covid-19 vaccine by January to continue attending school in person, making the school system the first large district in the country to mandate the shots for children.

The board of the Los Angeles Unified School District, the country’s second-largest district, voted unanimously on Thursday to pass the measure. One board member recused himself from the vote because of his stock ownership in Pfizer Inc.

“It seems to me that the safest way to protect children under 12 is for as many people as possible to be vaccinated,” said Jackie Goldberg, a board member during the meeting before the vote. “So I do not see this as your choice or my choice or about my great nieces and nephews and grandchildren or your children. I see this as a community necessity to protect the children under 12 who cannot be vaccinated.”

Before the vote, the LAUSD already had some of the toughest and most comprehensive safety measures in place compared with other districts, including weekly testing of students and staff, masking indoors and outdoors and a vaccine mandate for employees.

Despite those mitigation strategies, the district, which serves 600,00 students, is still vulnerable to disruptions because of the highly transmissible Delta variant, according to the resolution that the board passed. The resolution cited studies from the Centers for Disease Control and Prevention showing soaring infection and hospitalization rates in areas with lower vaccination rates.

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As of Wednesday, there were 1,357 active positive Covid-19 cases among LAUSD students and staff districtwide, according to the district dashboard.

About 57.8% of the 414,340 eligible district students ages 12 to 18 have received at least one dose of the vaccine as of Aug. 29, according to the Los Angeles County Public Health Department. The district began offering vaccine clinics at school sites on Aug. 30.

The district’s plan is to have all eligible students vaccinated by the start of the second semester. Students ages 12 years and older who participate in in-person extracurricular activities must receive their first dose by Oct. 3 and be fully vaccinated by Oct. 31. Others who are 12 years and older must receive their first shot by Nov. 21 and the second dose by Dec. 19. Those who turn 12 years old after those dates must receive their first dose no later than 30 days after their birthday. The Food and Drug Administration hasn’t yet approved Covid-19 vaccines for children under 12.

Students who don’t get vaccinated by the Jan. 10 deadline won’t be allowed on campus and will have to enroll in independent virtual learning, joining the roughly 3% of enrolled students who opted out of in-person learning this year. The students, from pre-K through 12th grade, who are enrolled in online learning receive daily live remote instruction from a teacher for part of the day, then complete assignments and other work independently.

A student receiving a Covid-19 vaccine at a mobile clinic at a high school in Los Angeles last month.

Photo: Jill Connelly/Bloomberg News

“Our goal is to keep kids and teachers as safe as possible, and in the classroom,” board Vice President Nick Melvoin said. “A medical and scientific consensus has emerged that the best way to protect everyone in our schools and communities is for all those who are eligible to get vaccinated. This policy is the best way to make that happen.”

The Los Angeles teachers union, which raised the idea of a student vaccine mandate weeks ago, welcomed Thursday’s vote in favor of the requirement. “We understand that many questions and concerns exist around the vaccine, but these questions should not take away from the critical step that will keep our schools safer and help protect the most vulnerable among us, including children too young to be vaccinated,” United Teachers Los Angeles President Cecily Myart-Cruz said in a statement.

While some parents called into the virtual board meeting to support the mandate, several others expressed hesitation and indignation that the district would mandate a vaccine.

“This decision should be made by parents, not by you,” Diana Guillen, a parent and president of the District English Learner Advisory Committee, said during the public comment period of the meeting. “We know if our children need the vaccine or not. It’s like you’re taking away our rights to care for our children.”

Public schools have long mandated certain vaccinations for students to attend school in person.

The Covid-19 vaccination requirement is indicative of how determined schools are to stick with in-person learning even as the virus has made a furious resurgence, forcing thousands of infected and exposed students and staff into quarantine just a month into the new school year.

The LA school district’s move on Thursday may lead to legal challenges. The vaccine manufactured by Pfizer and partner BioNTech SE is fully approved for people 16 and older but is only allowable under an emergency-use authorization for adolescents 12 to 15, which may complicate the district’s legal standing, according to Dorit Reiss, a professor at the University of California Hastings College of the Law.

Another question is whether the state’s elaborate immunization law means that districts cannot act in addition to what has been set out by the state, Ms. Reiss said. The state sets the law on school vaccine mandates, but school boards have broad powers to act for their schools, she said.

The district is already facing lawsuits from employees over its staff vaccine mandate and from parents over certain safety protocols.

California has a statewide teacher vaccination requirement that was approved last month.

Write to Yoree Koh at yoree.koh@wsj.com