The Federal Security Service (FSB) letter seen by RFE/RL on September 8 says that Pavlo Hryb is being held at a detention facility in Krasnodar Krai in southern Russia.
Hryb, 19, disappeared in late August after he traveled to Belarus to meet a woman he met online in what his father believes was a trap set by the FSB.
Hryb's father, Ihor, had previously said that he had learned "unofficially" that his son was wanted in Russia on accusations related to "terrorism."
But the copy of the FSB letter states the specific allegation that Hryb faces: abetting terrorism, punishable by up to 10 years in prison.
Read alsoUkraine MFA: Russia's FSB officially admits abduction of 19-year-old Ukrainian in BelarusThe statute cited in the letter covers recruitment, persuasion, and other efforts to involve another person in terrorism or a range of other antigovernment actions.
The letter provides no details about specific alleged crimes committed by Hryb.
Ihor Hryb has said his son was openly critical of Russian interference in Ukraine on social media.
The August 25 letter from the FSB's regional branch in Krasnodar was addressed to the Ukrainian consul in Rostov-on-Don, the capital of a Russian region that neighbors Krasnodar.
The letter states that Hryb was detained the same day on suspicion of abetting terrorism, though it does not provide details about how and where he was detained.
It states that Hryb is being held in a detention facility in Krasnodar, the regional capital. His father had told RFE/RL previously that his son was being held in the same facility.
The case has caused friction between Ukraine and Belarus, which said earlier that Hryb crossed into its territory on August 24 but that it had no record of his exit from the country.
The Belarusian Interior Ministry said on September 8 that its officers had not detained Hryb and that it was still searching for him in Belarus.
The Ukrainian Foreign Ministry on September 8 protested Hryb's detention and demanded that Moscow grant consular access to Hryb "and explain in detail all of the reasons for his detention."
The statement condemns what it calls Russia's "persecution of Ukrainian citizens in Russia and elsewhere, groundless detentions of Ukrainians, violation of their rights to have fair trials, and their convictions on fabricated and politically motivated charges."
Kyiv and Moscow have been locked in a standoff over Russia's seizure of Ukraine's Crimean Peninsula in March 2014 and Moscow's backing of armed separatists in a war that has killed more than 10,000 people in eastern Ukraine since April 2014.
In March, the European Parliament called on Russia to free more than 30 Ukrainian citizens it said were in prison or other conditions of restricted freedom in Russia, Crimea, and parts of eastern Ukraine that are controlled by the Russia-backed separatists.