The immigrants allegedly paid about $3,000 each for jobs at the bakery.
"It's difficult to say how long they had been doing this," said Jorge Guzman, ICE. "It's an ongoing investigation."
Margarita Avilez Hernandez, 52, the bakery supervisor, was arrested on suspicion of employing an illegal immigrant.
Alicia Ramirez, 36, a former supervisor, was arrested about during a traffic stop in the Palm Springs area.
Ramirez and Hernandez are both legally in the United States. However, both women face six months in prison and a $3,000 fine for each unauthorized worker if convicted.
All but two of the 51 alleged illegal immigrants arrested are from Mexico.
City News Service contributed to this report.