The International Olympic Committee confirmed the decision by Bogdana Matsotska on Thursday, and the Alpine skier's father said he and his daughter are "extremely angry at President Viktor Yanukovych."
It was unclear if Matsotska had already returned to Ukraine.
Oleg Matsotskyy, who also coaches his daughter, posted a message in Ukrainian on his Facebook page in which he assailed Yanukovych's latest actions.
"Instead of resolving the conflict through negotiations (which we had hoped he would when we left for Sochi), has drenched the last hopes of the nation in blood," the message read.
"In solidarity with the fighters on the barricades ... and as a protest against the criminal actions made towards the protesters, the irresponsibility of the president and his lackey government, we refuse further performance at the Olympic Games in Sochi 2014."
IOC spokesman Mark Adams said the Olympic body has been in touch with Ukraine's national Olympic committee following a clash between anti-government protesters and police in Kyiv that left at least 25 people dead and hundreds injured.
Ukraine's NOC posted a statement on its website saying that it was "shocked" by the violence at home toward its "loved ones" and doing its "best to honour them on the fields of play here in Sochi."
"We believe in the wisdom and integrity of the Ukrainian people! We believe that together we can save our country and find a way forward!," the statement added. "As athletes we compete together with honour and friendship here in Sochi. We will do so peacefully to honour our home, our country, our Ukraine."
Pole vault great Sergei Bubka, who heads Ukraine's national committee, has urged Ukrainian athletes to remain in Sochi as a sign of unity. But he has also said he respects the rights of athletes to make their own decision. There were suggestions that many more Ukrainian athletes would follow Matsotska's lead, but a Ukrainian Olympic official said that wasn't the case.
"I have the information that they are not leaving Sochi," said Illia Klymenko, head of the marketing department for the Ukraine Olympic Committee.
Matsotska, who finished 27th in the women's super-G and 43rd in giant slalom, was on the slalom entry list issued last Sunday. The official start list for Friday's event won't be released until after the team captains' meeting Thursday evening. The 24-year-old skier also competed for Ukraine in the slalom and giant slalom at the Vancouver Games.
Some Ukrainian athletes had expressed interest in wearing black arm bands to honour those who died in the conflict. The Ukraine NOC said Wednesday they were informed by the IOC that they would not be allowed to wear them, just as some Norwegian competitors were denied permission earlier in the games. But Adams said Thursday conversations never got to that point and Ukrainian officials "decided to do other things."
The team held a minute of silence and also laid out four flags with black ribbons on the left corner of each one.
Adams said the IOC tries to encourage individual expressions of grief away from the competition.
"The overall, general idea is that we try to concentrate on the sport. There are 2,800 athletes here," he said. "As you can imagine, there are a lot, sadly, a lot of people with personal tragedy in their lives. Some with big political tragedies, some with personal tragedies, friends, loved ones, some athletes, some nonathletes. The idea is to try to help them to find other ways, individual or collectively, to mark those moments."
AP Sports Writers John Leicester, Stephen Wilson and Howard Fendrich contributed to this report.
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