Rubio said her legislation, AB 752, would prohibit both penalties without due process.
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Rubio, a former teacher, said in some cases the behaviors of 3- and 4-year-olds are misunderstood, resulting in academic struggles and more serious problems in later years.
"We don't want them in the jail system later because of what we could have done in preschool," Rubio said.
In the El Monte City School District, the Jeff Seymour Family Center does not expel preschoolers.
The El Monte Police Chief joined Rubio and local educators to discuss a new report stating hundreds of children are being suspended or expelled from preschool.
School officials said early devolvement and support for kids, parents and teachers is crucial.
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"What does the parent do when they're expelled?" Rubio said. "There has to be some way we can help them in the classroom. We know that if kids are not in the classroom they don't learn."
Assistant Superintendent Cynthia Traino said providing helpful resources to the community can prevent harmful behaviors and ensure the success of all the kids.
Rubio said a disproportionate number of the kids being kicked out of school are African American.
"Eighteen percent of the early education population is African American yet they constitute 48 percent of the expulsions," Rubio said.
AB 752 has been sent to Gov. Brown in the hopes that he will sign it.