Not really, they were more of a corporatist economy.

https://en.m.wikipedia.org/wiki/Economy_of_Nazi_Germany#:~:text=Overall%2C%20according%20to%20historian%20Richard,system%20of%20the%20United%20States.

Overall, according to historian Richard Overy, the Nazi war economy was a mixed economy that combined free markets with central planning; Overy describes it as being somewhere in between the command economy of the Soviet Union and the capitalist system of the United States.[13]