Political unrest in Ukraine last week led to more than 80 people, primarily demonstrators, being killed in clashes with security forces.
The trouble saw Dynamo Kiev's Europa League fixture against Valencia switched to Nicosia.
Now the US match on March 5 will also be relocated from its planned setting in Kharkiv, a city in the east of Ukraine, to Cyprus, with the venue set to be named on Wednesday.
US Soccer said in a statement: "After discussions with the Ukrainian Football Federation, we have decided not to play in Ukraine on March 5 and are planning to move the match to a city in Cyprus.
"We are in the final stages of discussions with Ukraine and the Cyprus Football Association to determine the location and kick-off time. We hope to have confirmation on all the match details by Wednesday."
Ousted Ukraine president Viktor Yanukovych has reportedly fled to a pro-Russian area and a warrant has been issued for his arrest.