The day, if it were approved, would have resulted in a day off for staff members and students just a week before state math tests and immediately after spring break, the Star-Telegram reports.
Those voting against the observance because the day came too close to the TAKS testing and might harm instruction.
Proponent and trustee Gloria Peña, felt differently.
"This is something we need to do for our students. He is significant. He is important. Cesar Chavez is an important individual who helped the community, not just Hispanics," Pena told the Star-Telegram. "This is important to me. It should be important to you because it's about the students."
About 38 percent of the Arlington district's more than 63,000 students are Hispanic.