Police said both appeared likely to survive, the St. Louis Post-Dispatch reported.
The shooting occurred in a fourth-floor office at Stevens Institute of Business & Arts at about 2 p.m., police said. The shooter, described as a part-time student for several years, was apparently upset about financial aid.
Investigators said the student turned his gun on himself in a stairwell.
"He was familiar to faculty and staff," St. Louis Police Chief Sam Dotson said. "The victim and the shooter were familiar with each other. They knew each other. This did not appear to be random. It appeared to be targeted."
About 50 people were in the building at the time of the shooting.
Both victims were in surgery at 3 p.m. at St. Louis University Hospital, an hour after the shooting, investigators said.
Stevens has about 180 students. It offers both two- and four-year degrees in specialties like business administration and interior design.