Danone – which makes Aptamil and Cow and Gate baby milk powder - said supermarkets were introducing a limit of two cans per customer.
The limit was being introduced to prevent some people bulk-buying baby milk to sell on to China as 'unofficial exports'.
It said it was also increasing milk production to meet the shortfall.
A spokesman for Danone said: "We understand that the increased demand is being fuelled by unofficial exports to China to satisfy the needs of parents who want Western brands for their babies.
"We would like to apologise to parents for any inconvenience caused by this limit. We know that most parents only buy one pack at a time, so we hope that the impact of this limit on UK parents will be minimal.
"If parents are unable to find their baby's usual brand of milk, we recommend they try another local store or revisit the store on another occasion."
Supermarkets Asda, Sainsbury's, Tesco and Morrisons said they have limited purchases to two units per customer.
The BBC reports that foreign-made baby formula are popular in China, especially since a locally manufactured formula laced with the industrial chemical melamine killed six infants in 2008 and caused another 300,000 to fall ill.
Earlier this year, shops in Australia were forced to restrict sales of infant formula, as Chinese customers and tourists bought them in bulk to send them home or to sell them online.
Authorities in Hong Kong also introduced restrictions in February to prevent shortages, banning travellers from leaving the territory with more than 1.8 kg (4lb) of formula. Last month, 10 people were arrested there for trying to smuggle more than the allowed amount into mainland China.