Shortly after launching its offensive in Ukraine last year, Moscow outlawed criticism of the conflict and has detained and charged thousands of people for speaking out and protesting against the conflict.
In a statement, the Moscow Prosecutor's Office accused Jamala of posting a video last April in which she spread "false information" about Russia's actions in Ukraine.
It said Jamala was motivated by her "national hatred" of the Russian army and would be detained in custody if she steps foot in Russia.
"The criminal case will be sent to the Basmanny District Court of Moscow for consideration," it said.
Jamala won Eurovision in 2016 with her song "1944" about the Soviet deportation of ethnic Tatars from her native Crimea, drawing ire from Russian politicians who argued the entry was too political.
Her song narrowly beat Russia's entry in a nail-biting televote sequence that left Moscow in third place.
Russia was banned from competing in the contest by organisers last year after it launched its full-scale military assault on Ukraine.