To answer this question, from the outset there has to be a distinction between the German zones occupied by the Western allies and the Soviet occupied zone, i.e the parts that first became the Tri-Zone then the Federal Republic of German and the German Democratic Republic, respectively.
The source I'm using is Greif zur Kamera, Kumpel!: Die Geschichte der Betriebsfotogruppen in der DDR by Regine Schiermeyer. (Grab the Camera, Buddy (1), the History of Company Photography Groups in the GDR (2)). The pertinent chapter 2 is available on Google books
In the West there weren't outright bans so much as a prioritisation of access to limited stock of film. No outright ban on possession or use of cameras existed, you just had nothing to take photos with, or rather on.
Professionals needed to be accredited by the allies. (p.36)
One basic reason was that, in essence, the production of equipment and film pretty much stopped in 1945. For amateurs the situation had already been getting worse throughout the war years, with available film material prioritised for war propagande (p.35)
An interesting quote:
At the end of the war, most photographers had to take care that their
remaining cameras and equipment weren't commandeered by the occupation
troops or were lost by way of plunder and theft. About 70% of
privately owned cameras were, as was later estimated, lost through the
"effect of war and capitulation". (p.35)
When production slowly rolled on again, only 5% were allocated for
(German) civilian use. 30% went to the occupation forces and the rest
was exported for much needed currency. (p.36)
That 5% was itself prioritised:
- Health (X-Rays!)
- Scientific research and education (e.g. universities)
- Press and journalism
- Professional photographers
This shows that journalists and other photographers were already on the bottom of the pecking order.
The wishes of amateurs weren't even considered. (p.36)
In the East it was even more dire. An article in early 1947 in the East-German magazine Fotografie states that
there are no cameras for amateurs and there won't be any in the
foreseeable future (p.36)
Outside of the black market it was essentially impossible for an amateur photographer to obtain cameras or film.
It can be assumed, that amateur photographers all had other things on
their mind during these times than their hobby. (p.36)
The author of the Fotografie article phrased it quite drastically
It's not yet clear whether this may spell the complete end of amateur
And yet, the same article mentions that by 1947/1948 there were some fledgling beginnings. New and re-created photography clubs started within the collectivised companies. And that this was even supported by the higher-ups
It's a good sign that the superiors aren't trying to actively
suffocate a culturally valuable means of relaxation and entertainment
By 1948 there were 20 officially registered (3) photography clubs in the West and 18 in the East.
So, in summary, not even in the East was there a ban on photography. It was a matter of scarcity, the usual effects of war - including plunder by occupation troops - and the fact that people would rather pay for food than film.
(1) The word Kumpel also is used as a word for miner in German, the double meaning is likely intentional.
(2) The word Betriebsfotogruppen is one of those GDR terms, where everything was socialised and ultimately organised by the SED, the Communist Party.
(3) Which has nothing to do with allies. Germans love organising, and what would be called a club in English, is an Eingetragener Verein, i.e. a registered club