Stocks of major household brands such as Marmite, Flora and Persil detergent are running low at Tesco following a row between the supermarket and Unilever, one of its main suppliers.
The consumer goods company is believed to have demanded a 10% price rise due to the falling value of the pound against the dollar and euro, and halted deliveries to Tesco when the supermarket refused.
The move is understood to have hit online sales rather than products in store.
Brands affected include Surf washing powder and Comfort fabric conditioner, mayonnaise maker Hellmann's, Pot Noodle and Ben & Jerry's Ice Cream - none of which are available from Tesco's website.
Unilever refused to comment on the dispute, but chief executive Paul Polman warned in June that a vote to leave the EU's single market would increase prices for consumers.
He told Channel 4 that a vote to Leave would mean hikes in import duties on items such as dairy products, leading to price rises that would affect consumers.
A Tesco spokesman said: "We are currently experiencing availability issues on a number of Unilever products. We hope to have this issue resolved soon."
Liberal Democrat leader Tim Farron blamed the Government, saying: "The chaos around Brexit is now hitting our supermarket shelves. This shows the Government don't have a plan or even a clue."
Tesco last week revealed its half-year profits dropped by more than a quarter to £71 million after being hit by the sector's price war, though it recorded sales growth for a third quarter in a row.
Former chief executives of Tesco, Sainsbury's, Asda, Morrisons, Marks & Spencer and B&Q all warned ahead of the referendum that a drop in the pound - coupled with supply chain disruption - would cause prices to spike.
The Tesco stand-off with Unilever came just hours after former Sainsbury's boss Justin King said shoppers should expect price rises after the fall in the value of the pound since the Brexit vote.
Mr King said supermarkets would struggle to absorb the rise in the cost of importing goods because of the devalued pound, meaning consumers would face higher prices, the Guardian said.
Speaking at a conference in London on Wednesday, Mr King said: "Retailers' margins are already squeezed. So there is no room to absorb input price pressures and costs will need to be passed on."
He added: "No business wants to be the first to blame Brexit for a rise in prices. But once someone does, there will be a flood of companies because they will all be suffering."