There are a bunch of sources claiming he said it, but the earliest one I was able to find is a 1968 book The Arms of Krupp, which also gives it in German as "privates Unternehmertum könne in der Demokratie nicht bestehen". However, oddly enough, there don't seem to be much in the way of web hits for the German version. Although it's possible there's some spelling difference at work there. Anyhow, what earlier or primary evidence is that he said it, allegedly in a meeting with German industrialists?
I'm not sure what the German original says, but the English version in the Nuremberg files (vol VII, p. 558) has it as:
REPORT OF SPEECHES BY HITLER AND GOERING TO GERMAN INDUSTRIALISTS ON 20 FEBRUARY 1933, FOUND IN GUSTAV KRUPP'S FILE "PRIVATE CORRESPONDENCE 1933/34" [...]
Private enterprise cannot be maintained in the age of democracy; it is conceivable only if the people have a sound idea of authority and personality. Everything positive, good, and valuable, which has been achieved in the world in the field of economics and culture, is solely attributable to personality. When, however, the defense of the existing order, its political administration, is left to a majority it will irretrievably go under. All the worldly goods which we possess, we owe to the struggle of the chosen.
This was in the context of a 1933 meeting. It is still slightly confusing to me if that particular page is from the speech of Göring or that of Hitler at that meeting. I think it's Hitler's though, because on p. 561, there's a "GOERING — [...]" which seems to introduce his speech.
Thanks to xyldke for finding the German version of that Nuremberg file. (The document is tagged 203-D in the latter, while it's tagged D-203 in the the English files...) The quote in German (p. 42) starts with:
Privatwirtschaft im Zeitalter der Demokratie ist nicht aufrechtzuerhalten; [...]
I still don't have an explanation why the quote in German in the Arms book uses rather different wording.
Following @xyldke's comment on Fizz's answer, the German original says
Privatwirtschaft im Zeitalter der Demokratie ist nicht aufrechtzuerhalten; sie ist nur denkbar, wenn das Volk eine tragende Idee von Autorität und Persönlichkeit besitzt. Alles, was in der Welt an Positivem, an Gutem und Wertvollen auf dem Gebiete der Wirtschaft und Kultur geschaffen worden ist, beruht ganz allein auf der Bedeutung der Persönlichkeit. Wird die Verteidigung des Geschaffenen, seine politische Verwaltung, aber einer Majorität überantwortet, so geht es rettungslos unter. Alle Lebensgüter, die wir besitzen, verdanken wir dem Kampfe von Auserlesenen.
My translation (I'm a German native speaker):
Private industry/the private sector cannot be maintained in the age of democracy; it is only thinkable when the people (Volk) have a fundamental idea of authority and personality. Everything positive, good, and valuable that has been created in the areas of economy and culture is based solely on the significance of personality. If, however, the defense of these creations, their political administration, is given to a majority, it will perish hopelessly. All goods in life that we own we owe to the struggle of a selected few (Auserlesenen).
You can also use DeepL translate to obtain the following:
Private economy in the age of democracy cannot be sustained; it is only conceivable if the people have a supporting idea of authority and personality. Everything positive, good and valuable that has been created in the world in the field of economy and culture is based entirely on the importance of personality. But if the defense of what has been created, its political administration, is handed over to a majority, it will perish hopelessly. All the goods of life that we possess we owe to the struggle of the select.