The world’s best-selling toy firm said it had failed to predict an 18% boost in sales earlier this year which had put “strain” on its manufacturers.
The Danish company apologised and insisted it would try to ensure it was not “disappointing children”.
Experts said that while toy makers often complain of shortages before Christmas, Lego’s popularity following the Lego Movie and its Star Wars range meant demand was exceeding supply.
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John Baulch, publisher of Toy World magazine, said: “I can be sceptical of stories circulating in the run-up to Christmas talking about product shortages but I think this is absolutely genuine.
“Lego has had a hugely successful couple of years. Demand for products globally has really taken off and the simple fact is that it can put huge pressure on the production process.
“It’s very difficult for Lego to predict demand because it has such a wide range of products.”
Steven Reece, toy consultant at The Toy Verdict, said: “There probably is a capacity issue. Unlike other companies which use third parties for manufacturing, Lego do it themselves.
“Because it’s such an emotive issue, with parents being pestered for toys, it’s very rarely a cynical ploy.”
Gary Grant, the owner and founder of The Entertainer toy store chain, said their shelves were not as full with Lego as expected ahead of the busiest time of year.
“It’s a success story,” he said. “They are probably one of the most organised toy companies in the world in terms of production. They’re just on a roll.”
Lego spokesman Roar Trangbaek said retailers which had already made orders for the plastic brick sets will have their products delivered, but the company may have trouble fulfilling new orders later this year.
He added that “select countries in Europe” could be affected but refused to comment on whether that included the UK or which toys could be hit.
He told the Press Association: “We’ve seen huge demand for Lego products in the first half of the year, which is a great result for us.
“But it has put strain on our manufacturing facilities around the world. They are running at full capacity.
“In some markets, we may not be able to deliver orders made now and onwards. We will do our best to ensure we are not disappointing children.
“We’re very sorry if we can’t deliver what our customers ask for. It’s not a good situation for us, even though it’s great that we are making products that children love.”
Mr Trangbaek said Lego recorded an 18% growth in sales in the first half of 2015 compared to the same period last year.
“We do our best in terms of forecasting,” he said. “Our expectations, as well as our retailers, didn’t see this coming.”
Privately-owned Lego overtook Barbie doll-maker Mattel last year to become the biggest toy firm in the world.
Former England football captain David Beckham is among its fans after admitting last year that he plays with Lego’s Tower Bridge set to relieve stress.