Eighteen clinics were Monday being set aside in Hong Kong to treat children who may have been infected by tainted milk imported from China.

Seven special assessment centres will also open from Tuesday morning to do detailed examination on suspected cases with priority given to high-risk infants, Health Secretary York Chow announced.

Chow announced the opening of the clinics and assessment centres amid chaotic Monday scenes after a 3-year-old Hong Kong girl developed a kidney stone from contaminated Chinese milk.

The lone hospital previously assigned to deal all with cases of suspected infection from contaminated milk was overrun by hundreds of anxious parents and young children Monday.

The case of the first victim, who was released from hospital Saturday, triggered alarm among parents across the city who have been feeding their children with milk imported from China.

Supermarkets and shops across the city of 6.9 million have since the weekend been clearing their shelves of all milk products from China, causing a rush on imported milk from Australia and Canada.

Chow apologized for the failure to provide adequate clinics and said priority would be given to sick children when the 18 centres and seven assessment centres begin operations.

He also announced that Hong Kong would introduce a new ban on melamine, the industrial chemical added to milk that has killed four babies and thousands more sick in China.

Tests on imported milk in Hong Kong found a number of samples infected with melamine, including milk made in China by food giant Nestle.

"We have finished all the testing for infant milk formula," Chow said, "and those that do not fulfil our criteria have been taken off the market.

"As far as we are concerned, the infant formula remaining on sale (in Hong Kong) is safe for consumers."

The rising anxiety in the former British colony came as China announced Monday that nearly 53,000 infants and children had fallen ill from contaminated milk products.

More than 50 per cent of dairy products sold in Hong Kong are imported from mainland China.