The shootings occurred inside the hospital, which is a few blocks north of the city's downtown. Police spokesman Jacob Bettin declined to say where in the building the shootings occurred, but Omaha television station KETV reported that witnesses said it happened in or near the cafeteria.
Bettin said the officers shot the suspect, but he did not say what may have led to the shootout. He said police were first notified about the shooting at 9:19 a.m.
Hospital employees outside the center declined to answer questions from The Associated Press.
Investigators were looking into whether the gunman may have been involved in another incident with police hours earlier in the Omaha suburb of Ralston, Bettin said. He did not elaborate.
According to the Burt County Sheriff's Office, deputies went to the home of a domestic-assault suspect near the town of Tekamah, but the suspect had recently left the home with three guns in his GMC pickup truck. Tekamah is about 40 miles north of Omaha.
Officers in the Omaha suburb of La Vista found the suspect's vehicle and gave chase, but tailed off when it reached dangerous speeds. Shortly after 12:30 a.m., the suspect crashed in Ralston and fled the scene, they said.
Omaha police say they haven't determined that the domestic-assault suspect was involved in the hospital shooting.
After the shootings, police and security officers stood outside the hospital and stopped those leaving the hospital to check whether they had already spoken with investigators inside.
Patients with appointments were allowed in.
Bettin said the hospital remained in partial lockdown to protect the crime scene and evidence.
Creighton University Medical Center, which has 334 beds, is one of two trauma centers in Omaha. It has a network of nearly 300 physicians who practice in eastern Nebraska and western Iowa.