It's rare for there to be as clear a winner as in this case, and at least it is a book I have heard of, if not actually read. The book most frequently tagged Ukraine on both LibraryThing and Goodreads is also owned by far more users of both systems than any other book set in Ukraine. As with a lot of the Eastern European (and some of the Western European) winners, it's a story very much in the shadow of the Holocaust, a novel published in 2002 and adapted for a 2005 film starring Elijah Wood as the central character (who has the same name as the book's author). It is:
Everything is Illuminated, by Jonathan Safran Foer.
Next on the GoodReads ranking is a book for very young children - the first we've had aimed at that age range - which is a popular American adaptation of a Ukrainian folk-tale:
The Mitten, by Jan Brett
The book which is second most frequently tagged "Ukraine" on both systems is not as widely owned as the winner, and also has a substantial framing narrative set in England, but it was the one I personally thought might be the answer:
A Short History of Tractors in Ukrainian, by Marina Lewycka
The top-ranked author writing in Ukrainian is Andrey Kurkov.