"It is hurtful to read comments where people are hoping I break my neck or that God is punishing me for being 'anti-Trump,'" Vonn said in a post on Instagram on Tuesday.
Vonn, the most successful female World Cup alpine skier of all time, added she was trying to make the point during her CNN interview that Olympic athletes represent their nation and not any specific political party or individual.
Trump, who is often quick to respond to criticism from high-profile people, has not yet weighed in on Vonn's comments.
Vonn, who won gold in the downhill at the 2010 Vancouver Games but missed the 2014 Games in Sochi due to injury, said people overseas were perplexed at the way the U.S. had changed.
"You cannot pick up a newspaper or turn on the TV in Europe without noticing how people are questioning our direction," she said.
"It seems to me that we must lead with understanding and strive for unity in our relationships throughout the world."
The reaction to her comments had also illustrated how divided the country was, she said.
"We need to find a way to put aside our differences and find common ground in communicating," Vonn added.
"Is it wrong to hope for a better world? All of this is much bigger than skiing and the Olympics.
"I am going to take the next two months to focus on what I can do and right now that is competing for my country. In doing that, I will be hoping that we Americans can still be that 'shining city on a hill.'"
(Reporting by Rory Carroll; Editing by Greg Stutchbury)
