The parent, Lauren Roupoli, raised concerns over mask mandates for students.
Roupoli also accused one member of the Education Board of condemning parents as "selfish" for raising their concerns at board meetings.
Before she had time to conclude, Davidson cut across Roupoli to tell her she had run out of time to talk, but Roupoli finished what she was saying anyway.
A round of praise from other parents followed Roupoli's last statement, during which she said: "We are vocal because we are our children's biggest advocates."
After this applause, Davidson heard saying "f**k you" into a microphone.
The incident is the most recent in a chain of arguments across America about the right for parents to question administrators about COVID restrictions. Recently, the National School Boards Association published an apology for saying the arguments could amount to domestic terrorism.
Attorney General Merrick Garland praised the apology letter while calling for the FBI to investigate such parents.
KTLA reports that following the meeting, Davidson published an apology for her remark in which she said: "I reaffirm my commitment to serve our community with dignity and integrity, and I hope they will accept my sincere apology."
Davidson, who has two children, joined the Los Alamitos Unified School District Board in 2018. She taught students at both elementary and secondary school levels for 25 years.
According to the education board's website, she grew up in the area and came back to teach in 1980 after getting married.
Over the years, Davidson and her husband have been involved in several leadership posts, such as the PTA, School Site Council, sports, and Scouts.
At present, California has forced a state-wide mask mandate on roughly 6.7 million students - a resolution upheld by the California Association of School Boards and teachers' unions.
Earlier this week, a Minnesota school board chairwoman spurred ire after footage of her demanding parents to announce their home address if they want to speak at public meetings.