Subsequently, the baby tested negative for HIV, it added.
State-owned Shanghai Xinxing Pharmaceutical Company, the country's second largest pharmaceutical manufacturing firm, sold more than 12,000 units of intravenous immunoglobulin.
Medical institutions have been ordered by the National Health Commission to suspend the use of the faulty batch on Tuesday after health authorities in east China's Jiangxi province detected traces of HIV in it, according to reports.
The reports said 12,226 bottles of the product had been distributed to a dozen hospitals in different provinces.
Shanghai Xinxing Pharmaceutical has been instructed to halt production of the vaccine and to initiate an emergency recall.
The plasma is used for an immune therapy treatment for illnesses such as leukemia.
This is not the first case of HIV spreading through blood transfusions in China.
Intravenous immunoglobulin, a blood product, prepared from the serum of between 1,000 and 15,000 donors per batch is used for the treatment of low immunity that is triggered by conditions like blood cancer and hepatitis.
Public faith in China's health regulators has been shaken by previous scandals. As part of the fallout, four former officials with the China Food and Drug Administration - the body above the NMPA - are being investigated for corruption. Months earlier, faulty diphtheria, tetanus and whooping cough vaccines resulted in the government slapping a record penalty of an equivalent of 1.3 billion US dollars on the vaccine manufacturer, Changchun Changsheng Biotechnology Company.
Public outrage over such scandals has alarmed the leadership of the ruling Communist Party, moving it to respond more quickly and firmly than in the past, including bringing criminal charges and billion dollar fines.
Also see in the New York Times an op-ed by global health expert Huáng Yánzhōng 黄延中: If a government can't deliver safe vaccines for children, is it fit to rule? Chinese offices are largely shut for the week-long Lunar New Year holiday.
He told the paper that patients treated with faulty blood plasma may not necessarily be infected with HIV, because there was an anti-virus treatment in the preparation process. According to China's Ministry of Health, over 40 percent of people who gave blood at illegal centers - which numbered in the hundreds - became infected with HIV.
The Associated Press contributed reporting to this story.