Anna Korsun, who performs under the stage name Maruv, won the national finals on Sunday and immediately came under fire from politicians because she often performs in Russia.
Her tours in Russia became a toxic issue at home because of Ukraine's denunciation of Russia for the 2014 annexation of Crimea and its support of separatist rebels in eastern Ukraine.
The National Public Broadcasting Company demanded she sign a contract that would temporarily bar her from performing in Russia along with other stipulations. Maruv said the conditions amounted to "censorship" and she refused to sign.
Other groups that placed highly in the competition refused to replace Maruv.
The broadcaster said Wednesday it wouldn't choose a replacement "out of respect for the viewers' choice" and wouldn't take part in the May competition in Israel.
Although Eurovision aims at being non-political and a friendly conglomeration of pop music performances, politics often roil in the background.
Ukraine angered many Russians in 2016 when its Eurovision entry won the competition with a song about the 1944 deportations of Crimean Tatars by Soviet leader Josef Stalin. The next year, when Ukraine hosted the competition, it refused to allow Russia's entry into the country because she had traveled to Crimea without the permission of the Ukrainian government.