Deputy Prime Minister Dmitry Rogozin wrote on Twitter that the Eurovision result "showed supporters of European integration their European future: a bearded girl."
"There's no limit to our outrage. It's the end of Europe. It has turned wild. They don't have men and women any more. They have 'it'," nationalist politician Vladimir Zhirinovsky told Rossiya-1 state television.
"Fifty years ago the Soviet army occupied Austria. We made a mistake in freeing Austria. We should have stayed," added the leader of the Liberal Democratic Party, known for his outrageous statements.
Russia's entry, the Tolmachevy Sisters, came seventh.
Russia gave Austria five points — one more than it awarded Ukraine as the ex-Soviet neighbours are locked in a deadly crisis.
Russia last year adopted a controversial law banning the "propaganda" of homosexuality to minors, prompting condemnation from Western leaders and rights activists. Russia has also banned adoption of Russian children by foreign gay couples.
Popular hip-hop star Timati wrote on his Instagram account that Wurst's victory was the result of a "mental illness of contemporary society".
"I wouldn't like one fine day to have to explain to my child why two guys are kissing or a woman is walking round with a dyed beard and that's supposed to be normal," he said.
But Ukrainian drag act Verka Serduchka, who came second at Eurovision in 2007, strongly backed Wurst.
"To be honest, at the start it did shock me a bit, but when I saw it, I thought: why not? A person wants to express himself," said Andriy Danilko, who performs as Serduchka.
"In a way it probably is a challenge from Europe to us, but let's respect the winner. People don't judge a winner," Kirkorov said.said Andriy Danilko, who performs as Serduchka.
"We need to be more compassionate. I hate when people are bullied," Danilko told Rossiya-1 television.
"She is kind. Don't be mean to her. She is an eccentric. An eccentric with a beard."
Flamboyant pop star Filipp Kirkorov, producer of Russia's Eurovision entry this year, even suggested Wurst's victory should make Russians reconsider homophobic views.
"Maybe this is a kind of protest against some of our views in Russia. Maybe we should have a think. Maybe we shouldn't have such a categorical attitude to people of different sexual orientations," he told Rossiya-1 television.
"In a way it probably is a challenge from Europe to us, but let's respect the winner. People don't judge a winner," Kirkorov said.