A notice on the Xinjiang regional government's website said the death occurred in the prefecture of Bazhou, but gave no other details such as whether the person was a baby.
The latest reported fatality adds to three deaths confirmed on Wednesday by China's Health Minister Chen Zhu, who also said more than 6,000 babies had fallen ill.
The three deaths were due to kidney failure after drinking milk powder contaminated with melamine.
Melamine, a chemical normally used in plastics, was illegally mixed into milk products and has made its way into the baby formula of 22 Chinese dairy companies.
Six people have been arrested, five of whom were involved in adding melamine to milk, the official Xinhua's news agency has said.
The government has announced a massive recall of tainted products and launched comprehensive nationwide tests for melamine throughout the agricultural sector and not just the dairy industry.