The ASA has received 161 complaints about the campaign, which was created by DLKW Lowe.
The news comes amid existing investigations into Christmas ads from Boots for alleged "cruelty to animals" and Asda for "sexism".
Morrisons will have to defend the ad against accusations of sexism after an ASA spokesman said the creative had sparked complaints for "reinforcing outdated stereotypes of women in the home".
The main Christmas ad featured a set-upon mother battling to organise Christmas for the family in surreal scenes.
A separate 20-second execution has drawn the ire of animal charity The Kennel Club for a scene depicting the family’s pet dog eating a Christmas pudding.
Complainants have pointed out that ingredients in a Christmas pudding, including grapes, raisins, currants and sultanas, can be highly poisonous to dogs.
The Kennel Club has written an open letter to the supermarket expressing serious concerns about the scene.
Nick Sutton, health and information officer at the Kennel Club, said: "It is easy to forget that these foods are poisonous to dogs, especially as they are something that we can eat without any problems.
"As the Morrisons advert depicts, children often feed their dogs with food from their plates. By exposing children to this advert, it may encourage them to copy this behaviour and inadvertently poison their beloved pet dog."
A Morrisons spokesperson said: "Of course we’ll help the Advertising Standards Authority and we’re sorry that we’ve caused concern to some dog lovers. We would never run any advert that encouraged poor pet care and we were very careful to take veterinary advice prior to filming the advert and we ensured we had a vet present during filming.
"The veterinary advice we received concluded that there would be minimal, if any, risk to a dog of serious toxic reaction should a small amount, in relation to its body weight, of Christmas cake or pudding be consumed on a one-off basis. We certainly aren’t recommending that dogs should be allowed to eat Christmas pudding. The adverts were part of a wider story and we’ll be moving to the next phase this week."
This article was first published on campaignlive.co.uk
Called TV ad targeting on Twitter, and developed followings its acquisition of social TV analytics firm Bluefin Labs, it is designed to help marketers extend and enhance their TV ad campaigns.