A TV advert claimed a £70 Aldi shop would cost £98 at the "big four" supermarkets.
Morrisons and two members of the public complained the adverts did not make it clear Aldi's own-brand products were being compared with branded products.
Aldi said comparative advertising was a "well-established principle".
The German discount supermarket chain said consumers were likely to interpret the comparison as intended - the branded and fresh products from Tesco, Asda, Sainsbury's and Morrisons shown versus the Aldi products shown.
It said it believed consumers would know that its competitors stocked own-brand products which met the same need and would likely be cheaper and, in any case, on-screen text read: "Other supermarkets may sell 'own brand' products at different prices."
The ruling applied to two TV adverts and a press advert.
The adverts claimed a £70 Aldi shop would cost £98 at the "big four" grocers and compared a £33.04 Aldi basket with the equivalent at its competitors, which it claimed would cost £53.35.
A press ad read: "When it comes to the crunch, Aldi win every time. Other supermarkets go up, down, all over the place. But Aldi have 'everyday low prices', so you know where you stand."
The Advertising Standards Authority (ASA) said: "We acknowledged that Aldi stated they had not intended the comparisons to represent a 'typical' weekly shop, but to be a comparison between the pictured products only.
"Nonetheless, we considered that was how consumers would interpret the adverts rather than as a representation of the savings which could be made by switching from a largely branded shop to shopping in Aldi, and therefore assessed them on that basis."
Aldi's UK and Ireland chief executive Matthew Barnes said it was "extremely disappointed" with the "ambiguous and inconsistent" decision.
"The use of comparative advertising is a well-established principle and is firmly in the interests of consumers and encourages competition between retailers," he said.
"We will work within this new guidance from the ASA and continue to promote the significant price gap between Aldi's quality, award-winning products and their higher-priced brand equivalents."
Three Aldi adverts claiming customers could make significant savings were misleading, the Advertising Standards Authority has ruled.