The incident, which occurred at a student housing complex at the university around 11.30 a.m. on Friday, left an 18-year-old freshman student dead and the injured was sent to hospital in stable condition, Xinhua reported.
Investigators said that an argument may be the cause of the shooting.
The two suspects, unclear if they are TSU students, were detained by police but the third suspect remains at large.
The university was locked down for several hours and classes were cancelled for the remainder of the day.
The shooting is the third in recent weeks on or near the TSU campus, but it is unclear if the shootings are related.
On Friday morning, a shooting at Northern Arizona University also caused the death of one student and the injury to three others.
So far this year, a total of 48 shooting incidents have reportedly happened on a school campus in the country, and of those shootings, 27 were classified as attacks that resulted in injury or death.