The accident happened Sunday evening while scenes were being shot around the Finance Ministry in Berlin, which was once the Nazis' aviation ministry.
United Artists said 10 extras briefly required medical attention after falling off the truck, which the studio said was traveling at less than 10 mph when wooden slats gave way - sending them off the side.
"No one suffered anything more serious than cuts and bruises, though one of the extras was kept in the hospital overnight for observation," said a statement Monday from United Artists.
Police said a bolt on a side panel of the truck apparently came loose as the vehicle turned a corner.
"Tom Cruise was not there and the film director also wasn't there," said Berlin police spokesman Martin Grosse. He put the total number of injured extras at 11.
United Artists said the movie's main production unit, which includes director Bryan Singer and Cruise himself, wasn't filming at the time of the accident - and "it is not expected to have any impact on the production schedule."
Police opened an investigation of persons unknown on suspicion of negligent bodily harm, Grosse said. That is a standard procedure with workplace accidents in Germany.
Valkyrie stars Cruise as Col. Claus Graf Schenk von Stauffenberg, the aristocratic army officer executed after a failed attempt to assassinate Adolf Hitler in 1944.