The men are suspected of acting as secret agents for the purpose of sabotage, as well as agreeing to commit arson and bring about an explosion, federal prosecutors said in a statement.
The alleged plans fit a pattern in which Western officials have accused Russia and its proxies of staging dozens of attacks and other incidents across Europe since the full-scale invasion of Ukraine more than three years ago.
Two of the men - identified only as Vladyslav T and Daniil B - were arrested in different parts of Germany on Friday and Saturday, respectively.
The third, identified as Yevhen B, was arrested on Tuesday in the northern Thurgau region of neighbouring Switzerland.
The suspects were accused of telling "one or more people suspected to be acting on behalf of Russian state agencies" around March that they were prepared to carry out attacks on freight transport in Germany, prosecutors said.
The alleged plan was for the men to send packages that would explode or catch fire while being transported to Ukraine.
One of the suspects, Vladyslav T, dispatched two "test packages" in Cologne at the end of March that contained GPS trackers to scope out possible means of transport, according to prosecutors.
He was allegedly tasked with doing so by Yevhen B, who is accused of providing the contents of the packages via Daniil B.
German prosecutors did not elaborate further on what was in the packages or on how and where they were dispatched.
In a previous case in 2024, Western security officials suspect Russian intelligence was behind a plot to put incendiary devices in packages on cargo planes headed to North America, including one that caught fire at a courier hub in Germany and another that ignited in a warehouse in the UK.
"We know that Russia is trying by all means to destabilise Western democracies, including with deliberate sabotage and perfidious intelligence methods," German Justice Minister Stefanie Hubig said following the latest arrests.
