President Donald Trump described the 42 year old political strategist as an attorney when announcing her appointment last week, and Zacharia has referred to herself as a lawyer.
The questions began when a reporter asked her on Tuesday in which state she had passed the bar exam required to be an attorney in the US. Standing alongside the president, she replied: "When I moved to China." She does not appear to be registered to the bar in any state where she has lived.
White House communications director Steven Cheung defended her, saying she is "uniquely qualified and whip smart to help inform the American people."
In a statement this week, Zacharia said: "I practised international transaction law, with all the appropriate credentials." She also told the New York Times that when she first began appearing on cable news, she asked Pepperdine University, her law school, how she should identify herself. She said the university president advised her she could call herself a lawyer, but not an attorney.
Pepperdine confirmed Zacharia graduated from its law school in California in 2011. A law degree is not a licence to practise law in the US.
On Wednesday, Campaign for Accountability filed a complaint with the California State Bar Association seeking an investigation into whether Zacharia "repeatedly held herself out to the public as entitled to practise law without a licence to do so, conduct California law treats as a crime."
According to the Wall Street Journal, Zacharia took the California bar exam after graduating but did not pass. California's bar exam is widely regarded as one of the hardest in the US to pass.