One online shopper contacted the store via Twitter to complain, saying: "Suddenly, in the middle of the hottest part of the year there's a six-bottle limit on soft drinks."
The cap applies to online purchases of bottles and multipacks of Pepsi, Pepsi Max, Coca-Cola, Diet Coke, Fanta, 7Up, as well as Asda's own-label soft drinks.
It emerged yesterday that the bakery giant Warburtons has been forced to stop making crumpets at some plants, while the cider maker Thatchers has temporarily ceased production.
Warburtons uses CO2 in the so-called modified atmosphere packaging for its products, which is designed to increase the shelf life.
Soft drinks firms, brewers and cider makers cannot operate without the gas which is used to put the fizz into their products.
Pubs across the country have run out of several popular draft beers, lager and cider, including John Smith's, Amstel and Strongbow.
Even if they have stocks of beer in their cellars, publicans cannot get it to customers unless they have their own supplies of CO2 to pump it up to the bar.
The production of fresh pork and chicken has been curtailed over the last week because abattoirs do not have the CO2 gas needed to put the animals to sleep ahead of the slaughter process.
The gas is also needed for the packaging of some fresh meat cuts to extend their shelf life.
Chief executive of the Food and Drink Federation, Ian Wright, said: 'We will see fewer chicken dishes, fewer pork and bacon dishes.
"We'll see probably less carbonated drinks and certainly bakery and other things that benefit from what's called modified atmosphere packaging."
Mr Wright expects new supplies of CO2 to become available next week. However, it will take some time before it reaches food and drink producers.
The British Retail Consortium, which speaks for supermarkets, confirmed some products will be in short supply.
A spokesman said: "Issues remain with the supply of carbon dioxide across Europe.
"Retailers and suppliers are working hard to ensure food availability is maintained by sourcing suitable alternatives.
"We are aware of specific pressures in some areas such as carbonated soft drinks, beer, British chicken and British pork but the majority of food products are unaffected and retailers do not anticipate food shortages.
"However, it is likely that the mix of products available may be affected."
Asda explained the decision to ration products, saying: "Given the issues affecting the whole industry, we've proactively managed the supply of some products such as soft drinks to ensure we've got enough to go around."
Warburtons, which is based in Bolton, said just one of its plants – at Eastwood in Nottinghamshire – has been operating normally.
Two others – in Enfield, North London, and Burnley – are not producing any goods, while its Stockton-on-Tees factory has received a small supply of CO2 after being offline for days.
A spokesman said: 'While the focus so far has been on meat and beverages, the current CO2 shortage is having a much wider impact across the food industry – even everyday staples such as crumpets are affected.
"We are producing nowhere near the 1.5 million packs of crumpets we usually make each week and have had to suspend production at a number of our bakeries."
Somerset based cider maker Thatchers said the CO2 shortage has created difficulties for the entire drinks industry.
Managing director Martin Thatcher said: "Like many other drinks producers, we are now unlikely to receive any deliveries of CO2 until next week."
The Ei Group, formerly known as Enterprise Inns, which is the UK's biggest pub group, has admitted running run out of some big brands of beer in a number of its 4,500 properties.
Wetherspoon, which has almost 1,000 outlets, said many are temporarily without draught John Smith's and Strongbow cider.
Brewing giant Heineken has admitted being unable to get kegs of some big brand beers to pubs.
Holdens Bottling, which is based in the West Midlands and works with independent breweries and small soft drinks firms, has been forced to halt its production of 80,000 bottles a day.
The loss of production is a disaster for the business, which had been on course for its best sales period in the 75 year history of the company because of the World Cup and the good weather.
Operations director, Mark Hammond, said: "The CO2 is an absolutely vital component, it is the equivalent of diesel in the haulage industry.
"We use it to get the actual fizz in the product, but it is also used in the processing to, for example, purge the tanks and pipes.
"Without it there is very little we can do. I am not very happy at all at the way our suppliers have handled this. They just do not seem to care."
Britain's biggest food and drink wholesaler Booker has been rationing beer and cider suppliers to customers, who include small shopkeepers, cafes and hotels.
The company is owned by Tesco. Yesterday, a number of its own-label fizzy drinks, as well as Pepsi, Tango and 7UP, were listed as "out of stock" on its website, however the firm insisted it was unrelated to the CO2 crisis.
Waitrose said there was an industry-wide shortage of big brand soft drinks such as Pepsi and Coca-Cola.
Lidl confirmed that it has had problems. A spokesman said: "We anticipate that there will be shortages, but we are working closely with our suppliers to ensure, where possible, the impact on product availability is minimised."
