In an interview with DW's Sarah Kelly, Marina Litvinenko responded to Trump's open support for Russian President Vladimir Putin during the US election campaign and since he won the presidency.
She warned that the billionaire businessman had "very little" knowledge of history and foreign relations, adding that, "I hope he will learn it more quickly."
Litvinenko cautioned Trump that several other world leaders had beaten a similar path, in an attempt to rebuild ties with the Kremlin in recent years.
Efforts could be in vain
"Everyone who became president or prime minister has tried to make a good relationship with Mr Putin. For the past 17 years, we have so many stories of relationships that started in a good way, but when they finished, it was a disaster, because Putin wouldn't change his mind," she told DW.
In the weeks since his election, Trump has signaled a new strategic alignment with Russia, despite criticism of Moscow's maneuvers in the Syrian conflict, and ongoing US and European sanctions on Russia over its annexing of Crimea and involvement in the separatist war in eastern Ukraine.
Litvinenko has firsthand experience of the Russian leader's approach to dissent. Last year, a British inquiry found that her husband, Alexander - a former spy for Russia's Federal Security Service (FSB) - was poisoned in 2006 by two Russian agents with a radioactive substance, after he had fled to London and claimed political asylum. He died three weeks later.
The inquiry said his assassination was likely ordered by Putin and the former director of the FSB, Nikolai Patrushev.
Marina Litvinenko also spoke out about the recent suspected poisoning of another Putin critic.
Vladimir Kara Murza is on life support after being hospitalized earlier this month. The documentary filmmaker and senior member of the People's Freedom Party was also taken seriously ill in May 2015 - also due to suspected poisoning.
She said she doubted that a full investigation would be held to determine the causes of both instances of illness.
"My situation was different because I was in London, and I knew I would receive support. But Vladimir is in Moscow, and how can we be sure that everything will be provided in the right way?" she told DW.
Litvinenko also warned that the future of a serious challenger to Putin was in doubt after Russian opposition leader Alexei Navalny was this week found guilty of embezzlement, charges that he claims have been trumped up by the Kremlin.
Navalny had wanted to run for the Russian presidency, but may not be eligible now that he has a criminal record - a five-year suspended prison sentence.
"They (the Russian opposition) can't protest openly ... they can't say anything ... they can't put anything on a blog or on Facebook because they'll be arrested. It's the lesson (sic) of the Russian government since to make life as difficult as possible for the opposition," Litvinenko told DW.