His gender is listed as "female" in records from the New York State Board of Elections, according to screen grabs published by Wired.
The images suggest Mr Kushner, who is a senior adviser to the president, registered to vote in November 2009.
The former property investor has not commented on the news, so it remains unclear how the error occurred.
The mistake is unlikely to constitute voter fraud, as that requires the culprit to deliberately give false information.
