The interior ministry in the eastern state of Thuringia said police were investigating the fires at a depot in the city of Erfurt last weekend.
"We cannot say with certainty who was behind this attack," said regional Interior Minister Georg Maier, but "If it should be confirmed that a foreign power -- Russia for example -- has carried out a targeted act of sabotage, then this is once again an attack on our democracy".
"I condemn in the harshest terms such hostile actions on German soil," he added.
Germany has uncovered numerous cases of suspected espionage and sabotage in the country since Russia launched its invasion of Ukraine in February 2022.
Europe's top economy has been the second-biggest supplier of aid to Ukraine since the invasion began.
Images purporting to show the burning trucks were uploaded on Thursday to a Russian Telegram channel, with a caption saying that "our people" had set them on fire.
According to German media reports the incident happened on the night of June 21 and resulted in four trucks being destroyed, with two more lightly damaged.
The Russian Telegram channel also claimed the trucks were being repaired for the Ukrainian armed forces.
The Thuringia interior ministry said police were "aware" of the images and were investigating their "origin and authenticity".
A spokesman for the defence ministry refused to confirm this at a press conference on Friday, saying the trucks belonged to "logistics troops in the region".
Thuringia's interior ministry said the investigation involved exchanging information with security authorities in other parts of Germany, "in particular with regard to similar incidents elsewhere in the country".
A year ago several military vehicles were set on fire at the same site in Erfurt, and two weeks ago six such vehicles were burned in the western town of Soltau.
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