The case, filed in a Massachusetts state court, comes days after Amazon Prime Now drivers filed a similar lawsuit against Amazon.com Inc in California.
The level of benefits owed to workers in the on-demand economy has been the subject of litigation in the courts, and debate in the U.S. presidential race.
Like drivers in the Amazon case, Google Express driver Anna Coorey said in her lawsuit that she was hired by an intermediary courier service but is required to work only for Google during her shift. Drivers wear Google Express uniforms and are required to accept every delivery assigned to them during each shift, the lawsuit said.
That makes drivers employees under Massachusetts state law, attorneys for Coorey argue, who should be paid overtime and other expenses.
A Google spokesman could not immediately comment on the lawsuit.
Ride services Uber and Lyft face similar lawsuits from drivers, brought by the same law firm which filed the case against Google on Friday.
The case in Suffolk County Superior Court is Anna Coorey vs. Google Inc and Beavex Inc.