More than 33,000 people had signed an online petition at Change.org by Monday afternoon.
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.
Opposition Greens party lawmaker Omid Nouripour meanwhile called on Foreign Minister Frank-Walter Steinmeier to honour Urban with the national Order of Merit.
Police say 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 believe 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."
Amri is believed to have overpowered Urban in the hours before the attack, commandeering his lorry while holding him captive in the passenger seat, where 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.