The shooting occurred just before 3 a.m. in the 3300 block of Yellowstone Boulevard.
According to police, someone fired several shots into an apartment while four adults and two children were inside. Police say little Arianna was struck in the torso.
Floyd's sister LaTonya tells FOX 26 that Arianna suffered a bullet wound to the stomach and some pierced ribs.
LaTonya also said that EMS took hours to respond to the scene, so Arianna's father had to drive her to the hospital, where doctors allegedly told the family she may not have made it.
Arianna underwent surgery and is said to be doing great now and is recovering in stable condition at Texas Children’s Hospital.
Houston Police Department Chief Troy Finner released a statement on Tuesday afternoon regarding the incident.
"I am aware and have concerns regarding the delayed response time in this incident and have initiated an Internal Affairs investigation I ask for the city continue to pray for the child's full recovery and assist in providing information that would lead to the arrest of the suspect or suspects responsible."
Police say there is no suspect description or motive at this time.