The "Spell and go" competition invited people to collect and swap letters from codes on wrappers to spell the names of 26 possible holiday destinations.
The contest was promoted on its website and social media in May, and was presented by longstanding brand spokesman Gary Lineker.
Out of 112 complaints lodged with the ASA, many said certain letters were being withheld, while others reported problems with the Walkers website accepting codes.
Walkers told the ASA the contest was run fairly, but the watchdog said it was not satisfied with the "random swap" function which allowed participants to exchange letters within a pool on the website.
The ASA said the pool was only made up of "type two" letters, meaning C, D and K could not be won.
It added: "[The ad] must not appear again in the form complained about.
"We told Walkers Snacks Ltd to ensure that in similar future promotions they ensured that significant conditions for all aspects of the promotion were communicated to consumers."
In a statement, Walkers said the online swap tool "could have been clearer" and it will ensure all future promotions take the ASA's feedback on board.
A spokeswoman for Walkers added: "We’re aware some customers are disappointed that they haven’t been successful in winning a holiday.
"Twenty thousand holidays could have been won if all the promotional packs in the market had been played and we would have honoured all of those should that have been the case."