AP Photo/Andrew Harnik
The judge, identified by the Daily News as US District Judge Gonzalo Curiel, is overseeing a lawsuit against Trump University.
"I think the judge has been extremely hostile to me. I think it has to do with, perhaps with I'm very, very strong on the border - very, very strong on the border," Trump told Wallace.
"We have a very hostile judge. Now, he is Hispanic, I believe," he added. "And he is a very hostile judge to me."
Wallace seemed perplexed.
"Why even bring up that he's Hispanic? I mean, it does raise the question," he asked Trump.
Trump said he brought up the judge's ethnic background because the media reports on how Hispanic voters have an unfavorable opinion of his candidacy. Trump famously launched his campaign last summer while accusing the Mexican government of sending rapists and murderers across the border.
"Because you always bring it up, Chris. Because you always say how the Hispanics don't like Donald Trump. You always bring it up in your poll numbers. You say the Hispanics don't like Donald Trump. You're the one that brings it up," Trump said.
"I don't think I ever brought it up," Wallace replied.
At a Saturday rally in Arkansas, Trump had discussed the "Hispanic" judge while panning a lawsuit against Trump University, which critics accuse of being a scam.
"There is a hostility toward me by the judge - tremendous hostility - beyond belief. I believe he happens to be Spanish, which is fine. He's Hispanic, which is fine. And we haven't asked for a recusal, which we may do," he told his supporters.
Here's some background on the case against Trump's school, via The Washington Post:
About 80,000 people attended free introductory seminars held in hotel ballrooms across the country. About 9,200 of those participants then paid $1,495 for three-day real estate seminars, and nearly 800 paid up to $35,000 for all-inclusive packages that included one-on-one mentoring. Trump University changed its name to the Trump Entrepreneur Initiative in May 2010 - the New York State Education Department had deemed the "university" part of the name misleading - and, soon after, stopped operating.
The venture is still caught up in three pending lawsuits, including the $40 million suit brought by New York Attorney General Eric Schneiderman.