The club, which carries the name of a perennial first division team in the old East Germany, plays in the regional fourth division and is overshadowed by the recently-created RB Leipzig.
Lokomotiv said one of the coaches pushed the youngsters into making the Hitlerian salute with arm outstretched for the photo which then appeared in an internet forum.
“We have studied this incredible incident very closely,” said club president Thomas Loewe.
He added that the incident will be monitored with the local authorities.
“So that we meet our educational responsibilities.”
The Nazi salute is banned under the German penal code.