Whelan, 78, accepted an aggravated misconduct charge and was also fined £50,000 ($77,800), warned about his future conduct and ordered to undertake an education course. He has seven days in which to decide whether to lodge an appeal.
The FA's disciplinary commission found that Whelan had committed an aggravated breach of its rules because his comments included "a reference to ethnic origin and/or race and/or nationality and/or religion or belief."
However, the commission said it was "satisfied" that Whelan "is not a racist."
In an interview with The Guardian newspaper, Whelan defended his appointment of manager Malky Mackay, who is being investigated by the FA over claims he sent racist and anti-Semitic text messages to a colleague during his time at Cardiff City.
Referring to remarks allegedly made by Mackay, Whelan was quoted as saying it was "nothing" to call a Chinese person a "chink" and also said: "Jewish people do chase money more than everybody else."
He subsequently apologized for any offense caused and declared that he was not a racist, but vowed that he would "immediately resign" as chairman of second-tier Wigan if found guilty of using racist language by the FA.
He also made a bungled attempt to explain his comments by saying in an interview with the Jewish Telegraph that he had referred to Chinese people as "chingalings" when he was growing up.
Whelan's comments saw him branded a "racist" by Cardiff's Malaysian owner Vincent Tan, who sacked Mackay in December 2013.
But Wigan issued a statement reacting to Whelan's punishment in which it quoted the FA's disciplinary commission as saying: "We are satisfied on the evidence before us that Mr Whelan is not a racist.
It continued, "We are equally satisfied on the evidence before us that Mr Whelan did not intend to cause any offense by his comments.
"It is clear that he himself is very upset by the words he used and he moved very quickly to apologize publicly, plead guilty and begin to make amends."
The FA has yet to make the full findings of the case public.