A vote by members of the Verdi service industry union showed 97 percent of those who took part were in favour of industrial action, said Jörg Lauenroth-Mago, the union spokesman.
"We will not let go until we have a reasonable wage agreement," he said.
The union, which represents 520 of the 1,200 or so employed workers at the Saxon distribution centre, said it would begin planning one-day and several-day strikes to increase pressure on the company. Of the union members there, 92 percent took part in the strike ballot he said.
The union members are the first employed by Amazon.de to have taken this step. The firm employs around 9,000 people across Germany.
The workers may have a long fight ahead - an Amazon spokeswoman said on Friday: "Members of the German logistics centres get paid rates at the upper end of what is normal in the logistics industry."
A documentary film shown by broadcaster ARD in February was highly critical of working conditions at Amazon's warehouses in Germany, showing temporary workers who were paid low wages, and whose promises of getting a proper job were broken.
The film also shows foreign workers living in horrible conditions and being bullied by a security firm which has since been fired by Amazon.