The infants, from a rural area of northwest Gansu province, were all admitted in the past two months, Xinhua news agency said, citing doctors at a local hospital.
"It is rare for babies to get kidney stones, let alone so many babies at the same time," Zhang Wei, a doctor at the Gansu-based No.1 Hospital of the People's Liberation Army, was quoted as saying.
Parents told the hospital their babies had all been drinking the same milk powder, Xinhua added without mentioning the brand.
The provincial Public Health Bureau said further investigations would be carried out to find if there was any connection between the kidney stones and the milk powder.
Kidney stones are small, solid masses that form when salts or minerals normally found in urine crystallise inside the kidney.
If they become large enough, they can move out of the kidney, cause infection and lead to permanent kidney damage. In 2004, at least 13 babies in eastern Anhui province died after drinking fake milk powder that investigators later found had no nutritional value, a scandal that rocked the country and triggered widespread investigations into food and health safety.