No, they didn't. All industry was nationalized under the German Labour Front (a 32 million strong central organization for all industries) and the government had heavily regulated what companies could produce and sell, how to produce, what prices they could set, and even how much money they could make at any given time.
The Nazis were vehement anti-capitalists, in fact they saw it was "Jewish Propaganda" and believed that Capitalism and Marxism were two sides of the same coin created by the Jews to enslave the world.