China Central Television (CCTV) cited an unidentified former Dumex sales manager as saying the company had paid medical staff at a city hospital in Tianjin to promote its products.
Milk powder is a highly sensitive topic in China after a scandal in 2008 when melamine added to baby milk killed at least six children and left thousands ill.
This damaged the reputation of local firms and boosted international brands' market share.
Chinese authorities have been cracking down in recent months on graft in various industries, with foreign companies such as British drugmaker GlaxoSmithKline (GSK.L) and Germany's Bayer (BAYGn.DE) in regulators' sights. Autos, telecommunications and banks may come next, regulators have suggested.
Local and foreign-owned milk powder firms, including Danone, were fined a record amount in August for price fixing.
The former Dumex sales manager, cited by CCTV, said that that company gave several hundred thousand yuan in "gifts" to the hospital every year.
CCTV said the man had a document detailing payments to doctors, with their bank card details and amounts paid.
The document, which CCTV said it had seen, showed staff at the hospital had received about 300,000 yuan ($49,000) in total each month from Dumex, with individual payments ranging from several hundred yuan to about 10,000 yuan.
"Dumex China pays great attention to and is extremely shocked by the CCTV report... We will immediately launch an investigation," Dumex said in a statement passed on by a Danone SA spokeswoman in Paris on Monday.
"Dumex Baby Food Co strictly adheres to Chinese laws and regulations," she said.
Corruption in China's healthcare industry is widespread, fuelled in part by low base salaries for doctors at the country's 13,500 public hospitals.
International guidelines, used in China, say doctors should promote breastfeeding unless there are medical reasons not to.
Mothers, meanwhile, were discouraged from breastfeeding, according to the CCTV report, which also quoted a nurse at the hospital as saying that formula-milk makers had been bribing them to recommend their products to mothers.
China is an important market for Danone's baby-nutrition division, which accounted for 20 percent of overall revenues in 2012. Danone praised "a very strong performance" in China in its annual results statement, citing the success of "a complete revamp of the Dumex range".
Danone had a 9.2 percent share by retail value of China's $12.4 billion formula milk market in 2012, according to data from market research firm Euromonitor.
