Babies who took the drug exhibited fever, diarrhoea, vomiting and inability to pass urine.
"The children died in spite of dialysis treatment because the kidneys were already damaged," Akunyili said.
She said that her agency, the National Agency for Food and Drugs Administration and Control (NAFDAC), was making every effort possible to address the problem, including urgently importing an antidote and pulling the tainted medicine off the shelves.
Akunyili said the NAFDAC had visited 1,675 drugs outlets, pharmacies, patent medicine stores, market stalls, clinics and hospitals, where 425 bottles of "My Pikin" were recovered.
The agency has shut down Barewa Pharmaceuticals, the Lagos-based manufacturer of "My Pikin", as well as a company called Tranxell Ltd, an un-registered firm that supplied chemicals to Barewa and other local drugs and textile manufacturers.
The agency is also trying to track down the main importer of the chemical used in making the teething mixture.
More than 40 children aged between four months and three years have been hospitalised since the first case was discovered on November 3.
Health officials believe the number of cases could be higher as many parents in Africa's most populous country do not have access to basic health care for their children.
NAFDAC started testing more children's drugs last week for fear that different brands of cough and teething medicine may also have been contaminated with the toxic chemical.