Temple police say nobody else was hurt in the hourlong incident Sunday night at Scott & White Hospital.
Police on Monday identified the gunman as 54-year-old Larry Wayne Robards of Temple. Authorities are trying to determine what sparked the standoff.
A hospital spokeswoman did not immediately provide more details Monday.
Sgt. Brad Hunt says police around 6:45 p.m. Sunday responded to a call about an armed man. Several hospital staffers were being held hostage in the emergency room common area.
Police had started negotiations when a hostage tried to grab the suspect's gun. A Temple officer fatally shot Robards to end the struggle.
Temple is 50 miles north of Austin.