"This incident is a hate crime in accordance with Texas laws," police in Plano, Texas, where the incident occurred, said in a statement on Saturday.
"This incident may also be a hate crime based on federal law, and we are working closely with the FBI and the Department of Justice Civil Rights Division on this case."
In a video of the incident, which was shared on social media and got millions of views, the woman was seen shouting racist comments in a parking lot at a group of four women of Indian origin.
"Go back to India, we don't want you here," she said in the video. "I hate you fucking Indians," the woman, who identified herself as Mexican-American in the video, added.
The arrest of the woman took place on Thursday. The video of the incident from Wednesday went viral on social media, particularly in India and the United States.
Police said the woman, Esmeralda Upton, was arrested on one charge of "assault bodily injury" and one charge of "terroristic threats." She was held on a total bond amount of $10,000.
One of the Indian women, Rani Banerjee, said she and three of her friends had just finished dinner at a restaurant when the woman confronted them in the parking lot.
"Suddenly, we heard this woman yelling at us and started coming toward us. We were shocked by the racial slurs that she used and combative attitude," Banerjee told an ABC News affiliate. Banerjee started recording the incident with her phone.
The video also appears to show Upton hitting the women.
"What was so very scary is she came very close and not only verbally assaulted us but started physically assaulting us. She started hitting me," Banerjee said.
A representative of Upton could not immediately be reached for comment.