The Port's other three marine terminals are effectively shut down for trucks as well, the Port of Oakland told CNBC, while there are some vessel labor operations underway.

This is the third-day truckers have protested California's gig worker labor law, which was sparked by the rise of gig economy platforms like Uber, Lyft and DoorDash. A two-year legal stay was recently lifted when the Supreme Court decided not to hear a case which would have protected truckers from the impact of the law.

AB5 requires companies that hire independent contractors to reclassify them as employees, but there are some exceptions in the law across industries. The majority of truck drivers in California are owner-operator and many in this job category are concerned about their future. An estimated 70,000 truckers who own and drive their own trucks would fall under this law and they do not want to become an employee or part of a union in order to work.