Sources tell Deadline the scene involved a stunt car crashing into a cargo crate, but instead of coming to a stop, the vehicle then rolled into an area set up for producers and directors to monitor filming on the San Pedro, California set.
"I can confirm there was an accident," Lieutenant Philip Heem of the Los Angeles Port Police tells the website.
"We had two injuries, one being worse than the other," he continued.
Both victims were hospitalised, although one was reportedly discharged on Thursday night.
Further details about the injuries sustained or the identities of those involved have not been released.
Authorities at the Occupational Safety and Health Administration were notified of the incident, and are expected to investigate the circumstances leading up to the accident to determine if there was anything that could have been avoided.
The crash prompted producers to postpone filming for the rest of Thursday and Friday. It's not known when work will resume, but they had been expected to wrap up scenes for the upcoming show's first season this weekend.
It wasn't the only mishap to happen on set on Thursday - Jessica took to Instagram to share a shot of her bruised left palm, after falling awkwardly during an action scene.
"Landed on my palm during shoot out w (with) bad guys (sic)," she captioned the Instagram Story post, to which she added, "ouch".
She and Gabrielle, who also serve as executive producers on the project, have yet to comment on the car stunt-gone-wrong.
"L.A.'s Finest" is an offshoot of the "Bad Boys" movie franchise, starring Gabrielle as her "Bad Boys 2" character Syd Burnett, fighting crime in Los Angeles with Jessica as her single-mother sidekick.
Network bosses at NBC initially passed on the project after viewing the pilot, but the police drama was subsequently picked up for a 13-episode, straight-to-series order by officials at Charter Communications last summer (18).
It will also feature Ernie Hudson, Zack Gilford, Duane Martin, and Ryan McPartlin, and will premiere exclusively on the Spectrum network later this year.