Texas A&M President Michael Young said the student will go through a disciplinary process that should take about 10 days.
The incident occurred Tuesday as the African-American and Latino students from Dallas were on a recruiting trip to the university in College Station.
A female Texas A&M student approached two high school girls and asked them what they thought of her Confederate battle flag earrings, said Sara Ortega, spokeswoman for Uplift Hampton Preparatory School. A counselor with the charter school students told them to ignore the comment and to keep walking.
Uplift Hampton Preparatory School junior Terquarie Wilson told CNN affiliate KTVT
that he thinks some other A&M students didn't like that one of the high schoolers was carrying a backpack with a University of Texas logo.
"They didn't like his bag, so they screamed, 'Go back to where you came from,' " Terquarie told the station. "And one of my peers turned around and said, 'You do realize we're all black or African-American, right?' "
Then people in the group of 13 white college students used a racial epithet several times toward the Uplift students, Ortega said.
, president at the university since May, wouldn't comment on whether the A&M student being investigated was in that group or was the other student with the earrings.
Earlier he said that campus police were investigating the incident. A&M tour guides reportedly called campus police. An officer who responded told the visitors that it appeared to be a case of people exercising First Amendment rights, then wrote a report.
Officials didn't immediately respond to CNN's request for the report.
, a state senator from Dallas, called on A&M students involved in the incident to be strongly disciplined and possibly expelled.
"They need to do the investigation, provide due process and make a decision. And it needs to be done swiftly, " he told CNN.
West said he has been pleased so far by the university's actions this week and in recent years on diversity issues.
"I know that there is a commitment to get more diversity (at Texas A&M), that they're not just idle words," he said.
According to a university demographics report from this past fall, Texas A&M's College Station campus is 3.6% black and 19.5% Hispanic or Latino. The university is 59.5% white, the report says
Joseph Benigno, the university's student body president, branded the incident "horrifying and disgusting" and urged students to speak out against any hateful comments or jokes they hear.
"It is time that we embrace the attitude that our silence does an extraordinary disservice to Texas A&M. Our silence fosters hate," he said in a post on the TAMU Student Government Association's Facebook page
Both the high school and the university are now taking steps to open the dialogue on race.
Ortega said the high school students met privately with school counselors to discuss the incident and held a school assembly with an outside facilitator that led a discussion about racism and diversity.
Young said he met with a "student-led inclusion council" that sought "input on how Texas A&M can improve in making all people feel welcome and safe on our campus."
Ortega said Uplift has been sending touring students to A&M for seven years. A group from another Uplift facility went Thursday without incident.