Assemblyman Das Williams, D-Santa Barbara, said no harm would be done under his AB131 because applicants also must swear under penalty of perjury that they are U.S. citizens.
By law, county election officials must now reject an application in which the space was left blank or spend time and money contacting the applicant.
"The point of this bill is just to make sure that someone is not turned away because they failed to fill out this box," Williams said.
The California Association of Clerks and Election Officials supports the bill. The group says many voters fill out a federal voter registration application that is accepted in California but does not ask for a place of birth.
Williams and the election officials say it's unfair to require voters to list their birthplace on a state application but not on a federal form.
The Assembly approved AB131 on a 47-21 vote over objections by Republican lawmakers. The legislation now moves to the state Senate.
"If this box is not important and the federal authorities don't have it, then why don't we remove it altogether?" said Assemblyman Tim Donnelly, R-Twin Peaks. "I don't really care what your national origin is. ... If you're an American, it doesn't really matter."
Williams said a place of birth might still be useful to elections officials to recruit poll workers with certain ethnic backgrounds or language skills to help on Election Day.
The bill also is supported by Secretary of State Debra Bowen, California Common Cause, the League of Women Voters of California and two labor unions. No organizations are recorded in opposition.