In the article, Mr Myers also argued that male presenters may earn more because they "work harder, get sick less frequently and seldom get pregnant".
Winkleman, who presents the Strictly Come Dancing, earns between £450,000 ($786,900) and £499,999 ($874,000), making her the eighth overall highest paid. She is the best paid female presenter, and the only woman to appear in the list of the corporation's top ten earners.
Feltz, a veteran broadcaster who presents radio shows on BBC Radio 2 and BBC Radio London, earns between £350,000 and £399, 999 is the joint fourteenth highest earner overall.
Gideon Falter, chair of Campaign Against Anti-Semitism, has complained to Ipso, the press regulator, about the article. "This was an utterly vile column which deployed well-worn anti-Semitic tropes about Jews," he said.
Mr Falters said that the article has breached clauses 12(i) and 12(ii) of the Editors' Code by making discriminatory comments about Jews and also mentioning the religion of the Jewish BBC presenters at all.
Mr Myers previously been criticised for writing articles in the Belfast Telegraph and the Irish Times claiming that "there was no Holocaust".
He also questioned the death toll of six million Jews, saying that activists had bought this number into "popular perception".
Another of his articles, titled "Africa is giving nothing to anyone - apart from AIDS", was printed in the Irish Independent.
A spokesman for the newspaper confirmed that Kevin Myers will not write again for The Sunday Times Ireland and that printed apology will appear in next week's paper.
"The Sunday Times editor Martin Ivens has also apologised personally to Claudia Winkleman and Vanessa Feltz for these unacceptable comments both to Jewish people and to women in the workplace," the spokesman said.
Mr Ivens said that the comments "should not have been published", adding: "We sincerely apologise both for the remarks and the error of judgement that led to publication."
Frank Fitzgibbon, editor of the Sunday Times in Ireland, also issued a statement apologising "unreservedly" for the article, saying he takes "full responsibility" for its publication.
"It contained views that have caused considerable distress and upset to a number of people," he said. "As the editor of the Ireland edition I take full responsibility for this error of judgment. This newspaper abhors anti-Semitism and did not intend to cause offence to Jewish people."
This is not the first time that The Sunday Times has been accused of printing anti-Semitic content. In 2013, Rupert Murdoch issued a "major" apology for a "grotesque, offensive" cartoon which was printed in the newspaper.
The cartoon, which depicted Benjamin Netanyahu, the Israeli Prime Minister, building a wall using what appeared to be the blood of Palestinians as cement, was published on Holocaust Memorial Day.
The Board of Deputies of British said the cartoon, was "shockingly reminiscent" of pictures used in "the virulently anti-Semitic Arab press", and evoked the "blood libel," a persistent myth that Jews secretly use human blood in their religious rituals.