The incident occurred at the grocery store near Sahara and Eastern avenues around 2:49 p.m.
Police said the driver drove about 80 yards into the frozen food section of the store before taking out registers, and landing near the meat section.
Seventeen people were treated for minor injuries at the scene, and nine people were transported to a local hospital. One of the nine was said to be listed in critical condition.
Investigators were reviewing surveillance video and working to determine if the driver was impaired or suffered from a medical episode.
ABC News contributed to this report.
