The former Respect and Labour Party MP likened the find to the “pristine” passports of the 9/11 perpetrators hours after the attacks.
It comes after police launched a manhunt to find Christmas market attack suspect Anis Amri after initially arresting and then releasing a Pakistani man.
Speaking on talkRADIO, Mr Galloway said: “What about the story that the real killer’s ID was in the cab of the car all the time.
I only ask because if you were about to commit an act of mass murder, would you even have your ID card on you?
Mr Galloway questioned why a “mass murderer” would keep an ID card while carrying out the Berlin terror attack.
“I only ask because if you were about to commit an act of mass murder, would you even have your ID card on you? And if you had it on you, would you leave it in the truck for the police to find?” he asked.
“Even if it took them rather a long time to find it.
“Because, if it’s untrue you see, it illustrates another deep flaw, a sickness even, at the heart of this whole confrontation which we’re involved between the West and the so-called ISIS and Al-Qaeda and their ‘soldiers’ that we can now expect to be popping up in European cities in greater and greater numbers.”
He then bashed Britain and other European nations for “funding terrorists in Syria”.
Mr Galloway said: “If you say someone’s a deadly mass-murdering terrorist when they kill civilians in Berlin, you’ve got some explaining to do when taxed with the fact that you’re giving guns, money and propaganda [and] support to exactly the same dastardly mass-murdering terrorists in Syria, which is exactly what Germany and France and Britain and the United States has been doing.”