The ad, created by Delaney Lund Knox Warren (DLKW), shows actor Robert Lindsay pushing a shopping trolley along a river.
Lindsay asks: “Does it have to cost a fortune every time you want some fresh fish? I just want a decent choice from a sustainable source?”
Sainsbury’s and four members of the public complained to the Advertising Standards Authority (ASA) that the comment about sustainable sourcing could not be substantiated.
Three of the complainants said the ad misleadingly implied that the cod was sourced sustainably.
A spokesman from the ASA says the case was “informally resolved” and Morrisons agreed to not show the ad again in its current form.
A spokewoman for Morrisons says it agreed to pull the ad until it can prove its claims, adding “which on the basis of our evidence we are confident will be achieved soon”.
“We stand by our claim that we offer a great value range of sustainable fresh fish,” it says.