The other student is alive, ABC news quoted Brewster County Sheriff Ronny Dodson as saying. Dodson said an officer responding to the scene was shot in what appears to have been an accident.
Meantime, the Brewster County Sheriff's Office told Reuters that there was "an active shooter incident" at Alpine High School, but declined to give further details.
Ruth Hucke, a spokeswoman for Big Bend Regional Medical Center in Alpine, told The Associated Press that hospital personnel were tending to three "victims."
Hucke declined to say how the victims were injured or further identify them.
Hucke said the hospital would provide a statement later Thursday.
Dodson told radio station KVLF that the injured student ran outside seeking help and was taken to a hospital with injuries that weren't considered life-threatening. He also said a federal law enforcement officer who was responding to the incident was shot in the leg when another officer's gun accidentally discharged, and that the officer's injuries aren't life threatening.
Dodson said the high school shooting was part of a chaotic series of events that included a bomb threat called in at nearby Sul Ross State University, which required law enforcement personnel to rush there from the high school.
"That's ridiculous for someone to call in something like this when we've got this situation going on," Dodson said. "This community does not expect this, we don't want this, and we can't explain it yet."
Local TV station KWES reported that students said they heard two or three shots.
The Alpine Independent School District website says the town of about 5,900 residents has three schools — elementary, middle and a high school.
Alpine is 355 kilometres southeast of El Paso.