The instructor was let go under a provision that permits the immediate dismissal of personnel who violate service obligations, or whose continued service would harm the order or reputation of the military, a ministry spokesman said on condition of anonymity, as is customary.
The incident, captured in footage posted on the Internet, led the Bronx borough president to call for discipline against those responsible.
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 between bursts. The instructor then tells the soldier to curse even louder.
The Defense Ministry on Monday described the incident as "completely unacceptable" but said an investigation could take several weeks.
The instructor, whom authorities have not named, has admitted being the person in the video, the ministry said. The soldier who made the video is also being investigated.
In New York, Bronx Borough President Adolfo Carrion Jr. demanded an apology.
"The German government obviously has work to do to correct something that is insidious. ... Clearly these folks don't know anything about African-Americans or the Bronx," he said Saturday, after the video was aired on German television.
The incident is the latest embarrassment for the German military.
A group of army instructors is currently on trial on charges they abused and humiliated recruits in 2004. Last year, newspapers published photos of German soldiers in Afghanistan posing with skulls — including one soldier who exposed himself.