Ellen Gilland, 76, told officers that her husband, Jerry Gilland, 77, had been ill for some time and they had worked out the plan together, police spokeswoman Carrie McCallister said.
After shooting her husband around 11:30 a.m., the woman refused to leave the room until around 3:30 p.m. after negotiating with police, McCallister said.
Ellen Gilland did not harm herself and no one else was hurt.
Part of the hospital was evacuated and some doctors, nurses and other staff took refuge in closets and rooms.
McCallister said no charges have been announced at this time.
AdventHealth officials have not responded to an email seeking comment.