Modern Germany has really no ties to the Teutonic order in the form of a continued government. The Polish-Teutonic war, which began in 1519 and lasted 2 years, effectively ended the Teutonic order's power in Prussia. The order secularized into the Ducky of Prussia, a vassal of Poland. It's northern holdings in Livonia (now Latvia) going pretty much the same way. Eventually, the Duchy of Prussia is inherited by the Hohenzollern's of Brandenburg, an elector in the HRE. This is the beginning of the Brandenburg-Prussia (known as Prussia) that would become the largest power in northern Germany. In 1871 under Bismarck and Wilhelm I Prussia be the driving power behind the founding of the German empire, the first real modern incarnation of a modern Germany.

The order did maintain holdings in the HRE though, nothing that could really be said to tie to modern Germany. In 1809 the order was officially dissolved by Napoleon and their holdings in the HRE were given to France's many vassals.

Source: Germany 1866-1945 by Gordon Craig