A video of the incident, which the army said it is investigating, aired on German television Saturday and prompted calls for an apology by the Bronx borough president.
Defence Ministry spokesman Thomas Raabe condemned the episode, but said he believed it was an isolated case.
“This behaviour is absolutely unacceptable and contradicts the training standards of the German army,” he said at a news conference.
“We have a success story for more than 50 years in our German army and it is really seldom that something like that happens. I think it is not a special German problem,” he later said.
The German military, or Bundeswehr, was founded in West Germany in 1955, more than 10 years after the collapse of the Nazi government at the end of World War II.
Raabe said the army would likely complete its investigation into the video, which initially appeared on the internet, in two to four weeks.
The clip shows an instructor and a soldier dressed in camouflage in a forest. The instructor tells the soldier, “You are in the Bronx. A black van is stopping in front of you. Three African-Americans are getting out and they are insulting your mother in the worst ways... act.”
The soldier fires his machine gun and yells an obscenity several times in English. The instructor then tells the soldier to curse even louder.
The video has vanished from the German myvideo.de website but has since appeared on Youtube.com.