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Rickmers, which manages the ship for Maersk said Iranian navy fired "warning shots" at Marshall Islands-flagged Maersk Tigris.
A strike could come as soon as Monday, according to a statement from Teamster affiliate Justice for Port Truck Drivers.
Most ships should proceed to berth immediately or within a few days, according to the Marine Exchange of Southern California.
The International Longshore and Warehouse Union said 82 percent of its members voted in favor of ratification.
Trade Promotion Authority, a bill that grants the president authority to conclude trade deals without congressional interference, moved forward in the Senate Thursday morning.
Together with Dynamex, the two units will offer final mile delivery in more than 70 markets.