One of the stabbing victims, a visitor, is still in critical condition.
Police identified the suspect as 22-year-old Kyron Rashaun Templeton, who fled the scene but was apprehended soon afterward.
Witnesses told KLTV that the suspect ran through the halls with a knife shouting, "You're not going to kill my mother."
"The Good Shepherd family tragically lost a member of our team this morning," Good Shepherd Health System president Steve Altmiller said in a statement. "All of the victims were taken to the emergency center for assessment and treatment."
"Today, in a place of healing, our medical community had to quickly move from caring for others to caring for us," Altmiller said later. "May this help each and every one of us as we remember we are a place of hope and healing. God Bless Gail, her family and all of us."
[NBC Dallas-Fort Worth, KLTV]