The friendly, previously scheduled to take place in Kharkiv, had been moved to Cyprus because of Ukraine's unstable political situation and after US requests.
Anatoliy Konkov, the head of Ukraine's football federation, said on Monday: "We cannot hold the national championship so what kind of football can we talk of at all? If we do not have an opportunity to play on home soil, why shall we go to Cyprus in those troubled times for your country?
"We play for our people and country. Our team do not fly to Cyprus and stay at home," he told the ICTV channel.
Ukraine's Premier League also postponed the restart of the domestic championship after the mid-season break following Russia's military intervention in Ukraine's autonomous region of Crimea.
However, US Soccer said on Twitter that the game would go ahead.
"The Football Federation of Ukraine confirmed that their team will travel to Cyprus and the match will proceed as scheduled," it said.
Russian President Vladimir Putin won permission from his parliament on Saturday to use military force in Ukraine. The stated purpose was to protect ethnic Russians following the ouster of Ukraine's Russian-backed president a week ago.
Putin got the green light from parliament after Russian forces had already gained control of Crimea, an isolated Black Sea peninsula with an ethnic Russian majority and where Moscow has long had a naval base.
The United States is preparing to impose sanctions on Russia for its military intervention in Ukraine's Crimea region although no decisions have yet been made, the US State Department said on Monday.
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