More than 33,000 people had signed an online petition at Change.org by Monday afternoon, demanding that Lukasz Urban be awarded the Federal Cross of Merit, the highest civilian honour, by German President Joachim Gauck.
Police initially said Urban was shot dead by the suspected jihadist attacker, Tunisian Anis Amri, shortly after Amri had ploughed Urban's 40-tonne truck through a crowd of revellers at a Berlin Christmas market on December 19.
Twelve people were killed and dozens injured, but investigators reportedly believed Urban prevented even more casualties by grabbing the steering wheel in a struggle with Amri and directing the truck back out of the crowd.
The Change.org petition said that "according to current reports, the autopsy shows that he struggled with the perpetrator and was severely injured and eventually killed by him".
"With this heroic act, he probably saved many lives ... For this bravery, he deserves Germany's highest decoration."
But a report in Bild on Tuesday contradicted this version of events.
Sources close to the investigation told the newspaper that the final results of the postmortem showed Urban had been shot several hours before the truck attack, indicating that he had not grabbed the steering wheel during the incident.
Amri is believed to have overpowered Urban in the hours before the attack and commandeering his lorry. The Polish driver was later found dead with a gunshot wound.
Amri went on the run after the deadly rampage and was the focus of a Europe-wide manhunt before he was shot dead by Italian police in Milan four days later after opening fire first.