The Los Angeles resident, a spa worker, pleaded guilty at her closed trial in the Urals city of Yekaterinburg, where her case was heard by the same court that convicted Wall Street Journal reporter Evan Gershkovich of espionage in July.
The court said investigators found that on February 24, 2022 - the first day of Russia's invasion of Ukraine - Karelina had "transferred funds in the interests of a Ukrainian organisation, which were subsequently used for the purchase of tactical medicine items, equipment, means of defeat and ammunition by the Armed Forces of Ukraine".
Her supporters say she had donated $US51.80 ($A78) to Razom for Ukraine, a New York-based charity that provides humanitarian aid to children and elderly people in Ukraine.
The charity has denied it provides any military support to Kyiv.
Karelina, 33, appeared in court on Thursday in a white sweatshirt and blue jeans, sitting calmly in a glass courtroom cage.
She was not included in a major prisoner swap between Russia and the West two weeks ago that freed Gershkovich, but her lawyer, Mikhail Mushailov, has said she hoped to be included in a future exchange.
Karelina was born in Russia and emigrated to the United States in 2012 via a work-study program, receiving American citizenship in 2021.
She was arrested by the FSB security service after flying to Russia to visit her family in Yekaterinburg at the start of 2024.
Problems began immediately for Karelina when she arrived in Russia using her US passport.
Authorities interrogated her and took her mobile phone on which they found the 2022 donation to the charity, Razom for Ukraine, on her Venmo account, according to the website freeksenia.com.
The FSB interrogated her during weekly check-ins and banned her from leaving the city, the website says.
Three days before she was due to return to Los Angeles, Karelina was arrested on a hooliganism charges and jailed for 15 days.
Just before her release, she was slapped with a state treason charge.
Karelina's family and friends in the US have described her as someone who did not much care for politics and said they were shocked by her arrest.
Her boyfriend, Christopher van Heerden, told Reuters he had been in contact with the State Department and the US embassy in Moscow about securing her release.
Unlike in the cases of Gershkovich and former US Marine Paul Whelan, who was also freed in the swap in August, Karelina has not been designated by Washington as "wrongfully detained", a label that would open up diplomatic avenues to negotiate a prisoner exchange.
