Smith allegedly committed the crime in front of the French Press Coffee House in Chalmette, Louisiana, a suburb of New Orleans, on the evening of April 17.
St. Bernard Parish District Attorney Perry Nicosia reportedly issued the warrant for Smith's arrest.
Law enforcement officials said the incident was captured on video, per Mackel.
"We are aware of the reports regarding Aldon Smith. Aldon notified us, and we are gathering more information. We have no further comment at this time," a Seahawks spokesperson said in a statement.
Smith signed a one-year deal with Seattle on April 15.
The allegation is the latest legal issue for the former All-Pro edge rusher. The 31-year-old has been arrested multiple times since 2012 for charges related to driving under the influence. The NFL suspended Smith for nine games in 2014 for violating the league's personal conduct and substance abuse policies. Smith also missed four NFL seasons while serving multiple suspensions before returning in 2020 with the Dallas Cowboys.