Eagle-eyed officers at the border spotted a wooden box with holes inside her car, which she said contained beer she had bought in Mexico.
Officers opened the box and discovered the live spider monkey inside and directed her to pull over for a secondary inspection.
Valdez refused and sped off, running a traffic light and "nearly colliding with officers and other vehicles," officials said.
Investigators later found online ads for the sale of a spider monkey with her phone number listed.
Valdez turned herself in to law enforcement on March 28 and pleaded guilty to smuggling wildlife into the United States without first declaring and invoicing it and fleeing an immigration checkpoint on Nov. 2.
The monkey was taken to an animal shelter in Florida where it is "safely living," according to officials.
Valdez is scheduled to be sentenced in January 2023, and faces up to 20 years in prison and a $250,000 fine if convicted.
"Smuggling in endangered species for commercial gain is a tragic crime against nature's precious resources," said Craig Larrabee, acting special agent in charge for Homeland Security Investigations in San Antonio.
"HSI takes every opportunity to join our federal, private sector and international partners to share our knowledge, experience and investigative techniques designed to protect and preserve threatened and endangered species."