Mark Thompson, a former director-general of the BBC, is named in the class-action case alongside another executive, Meredith Levien.
The case was filed by two black female employees in their sixties.
It alleges that paper's ideal employee is young and white, with no family.
The two employees accuse the Times of "engaging in deplorable discrimination".
Their deposition says: "Unbeknownst to the world at large, not only does the Times have an ideal customer (young, white, wealthy), but also an ideal staffer (young, white, unencumbered with a family) to draw that purported ideal customer."
It goes on to list a series of allegations against Mr Thompson concerning his tenure at the BBC, and accuse him of perpetuating similar discrimination there.
At the time, Mr Thompson acknowledged that there were "too few older women broadcasting on the BBC".
Eileen Murphy, a spokeswoman for the New York Times Company, said in a statement that the suit contained "a series of recycled, scurrilous and unjustified attacks on both Mark Thompson and Meredith Levien".
She said: "We strongly disagree with any claim that the Times, Mr Thompson or Ms Levien have discriminated against any individual or group of employees. The suit is entirely without merit and we intend to fight it vigorously in court."
The case alleges that Ms Levien, who was hired by Mr Thompson as the company's chief revenue officer, said early in her employment that the paper's commercial department should be filled with "fresh faces" and "people who look like the people we are selling to".
The claimants, 62-year-old Ernestine Grant and 61-year-old Marjorie Walker, who both work for the commercial department, say that they and others like them have been "packaged out" of the department to make way for younger, whiter employees.
It comes two years after the dismissal from the New York Times of Jill Abramson, the newspaper's first female executive editor.
Mrs Abramson's sacking after three years gave rise to speculation that she was fired for complaining about being paid less than her male counterparts, an allegation that the company denies.
On a page on its website devoted to diversity, the Times says it is "committed to an inclusive and diverse workforce that reflects the audience, readers and advertisers we serve".
The chief executive of the New York Times is facing multi-million dollar legal action alleging he introduced an "environment rife with discrimination based on age, race and gender".