The Maricopa County Department of Public Health said the customers were infected with E. coli, a food-borne illness, after eating at Federico's Mexican Food in late July, The Arizona Republic reported Tuesday.
Two children, aged 4 and 17, developed hemolytic uremic syndrome, which can cause kidney failure, said department spokeswoman Jeanene Fowler.
Most of the 23 people hospitalized have been released, she added.
Bill Marler, an attorney representing 26 of the customers, said the children with the kidney disease will require monitoring for the rest of their lives.
The restaurant voluntarily closed Aug. 1 and reopened four days later after extensive cleaning.
Health officials said they have not yet identified what food item made the customers sick. No other restaurants in the area have reported similar problems.