Despite the fact the ad was authorised by National leader Judith Collins, Mallard said she has assured him that she did not see it before it was published.
Mallard said it was National's general manager, Greg Hamilton, who was responsible for the post.
Nevertheless, Collins has apologised and assured the Speaker that the material would not be put back on social media.
The ad included the text of a written question National's health spokesman Shane Reti had asked Health Minister Chris Hipkins.
It had a fake ministerial letterhead as well as the Labour Party's logo.
This, according to Mallard, was meant to "lend authenticity to the misrepresentation".
The Privileges Committee acts as the rulekeeper of Parliament and MPs are sent there if they go against the rules in a significant way.
However, since Collins apologised for the ad and has taken it down, Mallard said he does not intend to take any further action.
It was Hipkins who complained about the ad – he said it was an "alteration and misrepresentation of a reply to a written question," Mallard said.
This is not the first time National has been in hot water over its advertising.
In February, National lost an appeal to the Advertising Standards Authority over a Facebook ad they were forced to take down.
That was in relation to an ad criticising the Government's proposed clean vehicle feebate scheme.
Related Stories
Comments
Time to grow up National, it is not like you have had a stellar year and set a great example. Now we get childish behaviour that ought to have been left in the school yard.
First crusher's husband is running a whacko conspiracy Facebook page that hosts abusive memes of the Prime Minister. Now this incident.
These smell to high heaven of Cameron Slater.
Given his very close relationship with Collins I would not be surprised to find that he was out in the back room managing the National Party's election campaign strategy.
If he is expect a lot more of this sort of rubbish
So the ad was authorised by Collins, but she knows nothing about it? I don't believe her at all. Is she trying to be less honest than tRump?
And then we have a fraudulent document in the ad? How could anyone believe anything the Collins' National Party says?
They will do anything to win, and if they do win then the first thing they will do is open the borders and let the virus in. They will say that they won't, but you would be a real mug to believe them.
As a swing voter, National are not doing much to pull me their way and they are probably not doing a lot to impress their normal support core either. Both major parties are looking weak on the ground for quality candidates and besides those with red (Grizz) or blue blinders on there must be a good number of us wondering what is the least worst option to take us forward.
But hey...that's politics! At least you're not having to choose between Biden and Trump or what the poor benighted people of the once Great Britain were presented with last time, Johnson or Corbyn (shudder).