During remarks Thursday at a golf club in Orange County, California, Kasich - known for his folksy, plain-talking style - told a story about a note left for him by a Latina hotel maid.
"A lot of them do jobs that they're willing to do, and that's why in the hotel you leave a little tip," Kasich remarked, according to the Los Angeles Times.
Kasich, a second-term governor and former congressman, went on to tell a story from a day or so earlier in Los Angeles.
"This lady wrote me in my hotel there in L.A. She wrote this note. It said, `I really want you to know that I care about your stay.' Is that just the greatest thing?" Kasich said, according to the newspaper. "So, you know, we can learn a lot and she's Hispanic, `cause I didn't know it at the time, but I met her in the hallway - asked her if I could get a little more soap," he said chuckling.
Democratic presidential front-runner Hillary Clinton tweeted, in Spanish: "Otro producto del Partido de Trump - (at)JohnKasich. Hablar sobre los latinos no solo quiere decir hablar de propinas" - "Another product of the Party of Trump - John Kasich. Talking about Latinos doesn't just mean talking about tips."
GOP presidential front-runner Donald Trump faced criticism when he asserted during his July campaign announcement that some Mexican immigrants to the United States bring drugs and crime, and some are rapists.
Kasich campaign spokesman Chris Schrimpf said Kasich's comments were meant to be complimentary.
"He was talking about how great the service was and how we should respect everyone in our society no matter what their job or position might be," Schrimpf said.
The president and CEO of the U.S. Hispanic Chamber of Commerce said he didn't find Kasich's comments offensive.
"I think, first of all, it was a well-intentioned comment. In my personal observation of John Kasich, he still represents that compassionate conservatism that has very much a Ronald Reagan feel to it," Javier Palomarez said in remarks to Politico.