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.
President Trump was bombastic on the subject after the 2016 US election, tweeting that "millions of people" had "voted illegally", but without offering any evidence.
While Mr Trump won the election via the electoral college, he actually received 2.86 million fewer votes than Democrat Hillary Clinton.