USviewer: KBTX-TV reported police had to break up a confrontation among attendees of the speech at the Memorial Student Center and said other protesters lined the walls with fists raised.
Several groups protested outside before and during the speech by Spencer. Some silently held placards while others loudly chanted slogans.
KBTX reported police in riot gear were seen going into the student union.
After the event ended, campus police tweeted that two non-student arrests had been made.
Hundreds gathered at nearby Kyle Field to hear music and speeches highlighting diversity and unity as a counter to Spencer.
Performers and speakers were to include John Sharp, chancellor of the Texas A&M University system, Michael K. Young, president of Texas A&M University, football players Trevor Knight and Myles Garrett, and numerous student speakers.
Enhanced security from university police and local law enforcement agencies was put in place Tuesday night.
Spencer is the leader of the so-called "alt-right," a name embraced by some white supremacists and white nationalists to refer to themselves and their ideology, which emphasizes preserving and protecting the white race in the United States.
Spencer recently chanted, "Hail Trump. Hail our people! Hail victory," at a recent National Police Institute conference in Washington, D.C.
Spencer was not invited by the university, but by former student Preston Wiginton. According to the university, anyone can host an event at a public university and school officials cannot cancel the event. There were about 60 people on the guest list, which included white nationalists and people who said they wanted to peacefully challenge the speaker.
"Whites will be a minority in America by the year 2050," Wiginton told KAGS-TV. "I often wonder, will the non-white population be as altruistic as the white population has been? Will there be civil rights for whites? Will there be equal opportunity for whites? And I think white people, and it showed with Trump's election, are concerned about their future."