ARD public television said the video featured a hooded militant calling himself Abu Hamsa.
"To the European Union and all their allies who help the Americans, the Mujahideen are on their way to you, and Allah permitting, they will destroy you all," he says in the German language recording, according to a transcript from the IntelCenter in Washington.
The man also threatens the Netherlands and Denmark over controversial cartoons lampooning the Islamic prophet Mohammed.
In an email statement, IntelCenter's chief executive Ben Venzke said the video was released on April 12 by As-Sahab, Al-Qaeda's video production unit, with the title "How to Prevent a Repeat of the Gaza Holocaust".
A spokesman for the Federal Crime Office confirmed the video's existence, but added that Germany's terror threat assessment remains unchanged. "The content does not change anything about the current threat," the spokesman, Michael Albertz, told AFP.
Several German-language videos with militants threatening attacks have appeared in recent months, some of them attributed to an Uzbekistan-based Islamic extremist group believed to have ties to Al-Qaeda.
Four suspected Islamic militants went on trial in the German city of Duesseldorf on Wednesday accused of plotting devastating bombings against US citizens in Germany.
The group allegedly planned the attacks to punish Germany for its military involvement in Afghanistan, where it has about 3,700 soldiers fighting under NATO command.