Pavlo Gryb, 20, who suffers from cirrhosis of the liver and partial vision loss, urgently needs surgery and may die in a Russian prison, his family says. The EU has described him as disabled.
A spokeswoman for a military court in the southern Russian city of Rostov-on-Don, Alyona Katkalo, told AFP Gryb had been convicted of "complicity in terrorism".
Gryb disappeared in August 2017 in ex-Soviet Belarus where he went to meet a young Russian woman he had corresponded with on social media, his family says. He later resurfaced in a Russian pre-trial detention centre.
Russian prosecutors claim that Gryb sought to convince the woman to blow up an explosive device in Russia's Black Sea resort of Sochi.
Gryb – who has criticised Russian authorities for the annexation of Crimea on social media – denies the charges.
Kiev says the Russian authorities have abducted the young man, denied him medical treatment, and convicted him on "fabricated charges".
The European Union has called on Moscow to free the "disabled" Ukrainian, saying Russia detained him "without any clear charges".
On Friday, the EU said in a statement it expected Gryb "to be immediately released and granted access to the special medical treatment he needs."
– Urgent treatment needed –
His father said Pavlo suffers from portal hypertension, which causes cirrhosis of the liver, and urgently needs medical treatment.
"Given Pavlo's deadly disease, it's a death sentence," Igor Gryb told AFP, referring to the conviction.
"He requires urgent surgery or he will die."
His father added that his son had not received proper medical treatment during his trial despite having a fever during the hearings.
Gryb's lawyer Marina Dubrovina said the Ukrainian had gone on hunger strike, adding that he demanded treatment.
The Ukrainian foreign ministry said on Friday that Moscow "crudely violates human rights including a right to a fair trial and a right to life".
Ukrainian Foreign Minister Pavlo Klimkin said on Twitter: "Mercy, humanity, dignity – Russian invaders, Russian aggressors are not familiar with these words."
Ties between Kiev and its Soviet-era master Moscow were shredded after a popular uprising in Ukraine ousted a Kremlin-backed regime in 2014. Russia retaliated by annexing Crimea and supporting a separatist uprising in the east of the country.
The conflict has claimed some 13,000 lives.
Dozens of Ukrainians are held in Russian prisons, including filmmaker Oleg Sentsov, who is serving a 20-year sentence and refused food for 145 days last year.
