The German army has faced a series of scandals in recent years
In the grainy 90-second video, the instructor tells the soldier to swear as he fires his gun.
US civil rights leader, Al Sharpton, said it was outrageous to depict blacks as "target practice".
New York officials say they are saddened and frustrated that the Bronx district is depicted so negatively.
"Clearly these folks don't know anything about African-Americans or the Bronx," said Bronx borough president Adolfo Carrion Jnr, who recently returned from a trip to Germany to promote tourism to the district.
He has demanded an apology from the Germany military over the clip.
During the filmed training session, an instructor tells the soldier: "You're in the Bronx, a black van pulls up in front of you and three African-Americans get out and start really insulting your mother... act!".
The soldier then fires his gun several times and shouts obscenities in English, as the instructor encourages him to curse even louder.
The clip was filmed in a forest in July 2006, near the barracks of the northern German town of Rendsburg .
The German army said it has been aware of the video since January and was investigating it.
It is the latest in a series of scandals to hit the German military.
A group of 18 army instructors are on trial in the country accused of abusing and humiliating recruits during training in 2004.
Last year, German newspapers published images of German soldiers serving in Afghanistan posing with skulls.