The supermarket chain has issued a statement saying Kier would complete work on the Wadebridge site at Higher Trenant to make it safe and secure.
Work started at the end of March on building the 50,000 sq ft flagship store.
The decision is a blow to Kier’s Western and Wales division as well as Bristol groundworks contractor Dancourt.
The supermarket chain said: “We can confirm that work on our planned Wadebridge store will not be completed this year.
“We recently announced a small reduction in the number of new stores to be built in 2014 and have with regret decided not to progress plans.
“We will be reviewing our programme of new stores for future years and hope to be able to make an announcement about our plans for Wadebridge in the coming months.”