Amflora poses "no danger for human health or the environment," a ministry spokeswoman told AFP.
Agriculture Minister Ilse Aigner decided to give the go-ahead to the trials after an "in-depth examination" and talks with scientific and economic experts, the spokeswoman said.
Amflora is a potato modified to produce starch consisting almost exclusively of a substance called amylopectin which is used in the paper, adhesives, textiles, construction and cosmetics industries.
Berlin's decision comes two weeks after Aigner controversially banned a type of genetically-modified maize manufactured by US biotech giant Monsanto. Aigner said she was outlawing the cultivation of MON 810 maize - modified to be super resistant against crop-destroying insects - on environmental grounds.
But opponents of the decision noted that the European Commission, the EU's executive arm, had reported no environmental or health concerns linked to MON 810.