The Irish Press Council has received 35 complaints about the controversial Kevin Myers article.
Chairman Sean Donlon said the Sunday Times piece about equal pay is clearly anti-Semitic and misogynistic.
It has launched an investigation into the article
Mr Donlon said it will watch how the newspaper handles the situation closely.
"What we will do now is that we will watch to see what further action they will take in the next few days," said Mr Donlon.
He said that if the appropriate action is not taken, particularly in terms of appropriate apologies next weekend, that action will be taken.
"If that [an apology] doesn't happen, we will be in touch with them," he added.
Leo Varadkar and Vanessa Feltz, one of those mentioned in the piece, criticised the column as anti-semitic.
However, a group representing Ireland's Jewish community has come to the defence of Kevin Myers.
The columnist has been fired from his role at the Sunday Times following the article which commented on the BBC's release of the top earners in the company.
But the Jewish Representative Council of Ireland said branding the writer an anti-Semite is a "distortion of the facts".
In a statement, the council said his comments about two Jewish BBC presenters were "a real error of judgement".
But the it said Kevin Myers is not an anti-Semite, and has praised him for writing columns about the Holocaust over the last three decades.