Footage of the incident, which happened at a Houston area location of the fast-food chain, shows an unidentified man verbally blasting an employee named Maria.
According to ABC station KTRK, which obtained a copy of the video that was filmed by someone else in the restaurant, the man appears to be upset after Maria asked her manager if a coupon that he presented for a free hamburger was valid.
The man is heard speaking to another employee, saying that the female employee should "buy a ticket back to where you came from."
When the male employee, who is not identified, asks what was wrong, the customer said "she told my son no. She lied her ass off... she thought she could get away with it."
"Hey, you are going to get fired," the man is heard saying to Maria.
"Goodbye Maria. Buy you a ticket back to Mexico," he is heard saying as he walked away from the counter.
The woman who filmed the incident, whose name has not been publicly released, spoke to KTRK and told the station that she was with her 9-year-old daughter, who was afraid during the altercation.
Jack in the Box did not immediately return ABC News' request for comment.
This incident comes shortly after a lawyer was filmed in a Manhattan salad restaurant yelling at customers and employees for speaking Spanish. The lawyer, later identified as Aaron Schlossberg, threatened to call U.S. Immigration and Customs Enforcement in an effort to get the individuals "kicked out of my country."
Schlossberg has since issued an apology, denying that he is a racist and said that the way that he "expressed myself is unacceptable and is not the person I am."