The unidentified man was taken to the center as a patient at approximately 6:00 a.m. on Monday, Orlando Police Chief John Mina said during a press conference.
Mina said the man was calm after being taken to the hospital for a "medical condition," but began making threats to the hospital staff, which led the emergency room to a lockdown.
"He said he had a gun and would shoot anyone who came near him," Mina said.
Crisis negotiators were called to the hospital, but the man made "aggressive movements" when police officers approached him, according to a NBC News report. He was then shot dead.
"I think if patients nearby hadn't needed care right away, we would have talked to him longer," Orlando Police Chief John Mina said.
No weapon was discovered and no one else was hurt, according to the report.