"Now, we see aggressive rhetoric, aggressive behavior, aggressive propaganda, and informational wars," she said in an interview with Voice of America before Saturday's inauguration.
"The great Russian chauvinism, which is now increasing in Russia, mainly very much depends on the elite, who are trying to revive it, and this is very dangerous. So I'[m] not much sure it will be over in five years, because it will surely be specific to President [Vladimir] Putin."
Lithuania, a small Baltic member of NATO and the European Union, was joined in the Soviet Union with its massive eastern neighbor until its independence in 1991.
The annexation of Crimea caused anxiety in many of Russia's southern and western neighbors, and Grybauskaite said Russia's suspected involvement in Ukraine is a dangerous foreign relations move.
"It is very worrying. And it looks like it's not over. The same methods that are now used in eastern Ukraine -- the same threats, at least not directly military yet, but informational, cyber. Propaganda wars, already we are feeling ourselves in the Baltic states (and) Poland, for example."
She compared Russia's attempts to safeguard Russian speakers beyond its borders with justifications Germany made before World War II, and added the Crimea annexation was a wake-up call for NATO.
Lithuania is working to cut its dependency on Russian natural gas supplies, and will increase its defense budget to two percent of its gross domestic product, a NATO benchmark, she said.