Prosecutors say a replica Panzer 38(t) tank, which took part in a mock battle in central Siberia with a World War 2-era black and white cross stencilled on its side, was in breach of a law outlawing Nazi symbols.
The enthusiasts who staged the event say the allegations are absurd and accuse prosecutors of failing to understand the point of a historical re-enactment.
But Vladimir Tokarev, prosecutor for the Novosibirsk region, said: "If today we do not notice a cross on a tank, tomorrow we will be surprised to see that young people have appeared on the streets with swastikas on their sleeves.
"This is precisely why the prosecutor's office has given an instruction . . . to painstakingly check what aims this organisation is pursuing and who it represents."
"We cannot ignore such facts. Nothing can be trifling in this case," he said in remarks posted on his office's website.
The head of the Siberian chapter of the Russian Military History Social Movement, which represents re-enactment enthusiasts, said prosecutors were mounting a witch-hunt.
"To put it mildly, I am indignant. I'm speechless," Oleg Nelzin told Reuters in a telephone interview.
"You shouldn't try to find a crime where one just doesn't exist. The re-enactment movement has nothing to do with skinheads or neo-Nazis . . . The people involved in this are pretty grown-up, level headed and well-off."
"If there is a re-enactment, you need an opponent."
Critics have accused the Kremlin of using anti-extremism laws to stifle dissent since parliament in 2006 adopted new legislation widening the legal definition of extremism.
The Kremlin says it wants to safeguard hard-won political stability from radical groups that seek to sow hatred.
The new extremism legislation was used last year to bring criminal charges against a Russian academic who had written a book that was scathingly critical of President Vladimir Putin.