Someone asked a similar question not too long ago, so I'll repost the answer I did then here:

Although the Nazi propaganda machine is best known for the more serious stuff you mention, the use of humor was hardly unknown. You'll find a lot more information on the use of humor within the population to make sense of what was going on, and to tweak the regime subtly than you will state approved wisecracks, as they didn't use it too forcefully, but it was certainly there.

One of the most overt examples comes from the early war years. For a period of time on 1940, Goebbels was commissioning short comic pieces that were shown with the weekly newsreels. A popular series of these featured Tran, who was something of a worrisome defeatist, and Helle, who was a good, stolid party man assured in the final victory. The shorts were formulaic, with Tran being a worrywart, and Helle getting him back in line. A representative sketch that Herzog features goes as follows:

HELLE: That’s great that you finally bought a radio receiver. Now you’ll know what an interesting age we live in. You can follow the major announcements of the empire.

TRAN: And maybe I can tune in occasionally to foreign broadcasters.

HELLE: What? You want to listen to foreign radio?

TRAN: Sure, foreign news. From London, for example.

HELLE: London?

TRAN: Yeah. Do you know how to get London?

HELLE: I don’t know how to get London, but I know what you’ll get if you succeed.

TRAN: And what’s that?

HELLE: The clink, even prison!

TRAN: And if no one finds out?

HELLE: It doesn’t matter if someone finds out or not. A good German doesn’t do things like that.

TRAN: But you have to be aware of what’s around you.

HELLE: Of course, the foreign broadcasts tell the truth pure and unadulterated. Haven’t you ever heard about the news system used by our enemies? If you did, you’d know that everything they say is intended to weaken our capacity for resistance.

Let's be honest, it doesn't seem all that funny, the punchline basically being 'The Gestapo will toss you in prison for not being a good German!'. but Germans found them pretty funny anyways. Just not always as Goebbels intended! Informers reporting back to the Ministry let him know that for the most part, people sympathized with Tran in the various scenarios. The second series of comic shorts, "Liese and Miese", were thus scrapped before they ran, and "Tran and Helle" (if you speak German, you'll find some of the sketches Youtube).

Other less overt examples of Nazi approved humor exist too of course. With state control of the film industry after all, any comedy had to go through approval by the censors, and more than a few parroted various aspects of Nazi ideology. The 1939 Robert and Bertram for instance was a musical comedy rife with antisemitism, and a subtle way to use the light, casual medium to inculcate audiences with the state approved ideas of nefarious Jews. Filled with every negative stereotype you could think it, the director himself described it as a film with "strong anti-Semitic tendency".

Another comedy with a similarly dark message was also from 1939, The Gas Man, which like the "Tran and Helle" shorts carried the oh so funny message of "obey authority and be a good little Nazi". As with the newsreel shorts, it hit a little close to home, and the party leadership disapproved of how the Nazi state came out looking, resulting in limited release of the film. So the sum of it is that as far as state sanctioned comedy went, it was fairly uninspired. Not the Party's favorite way to communicate its message, comedic material which it did approve of nevertheless was intended to carry with it a pro-Nazi message, resulting in mostly antisemitic screeds and exhortations to fall in line.

Source

Rudolph Herzog. Dead Funny: Humor in Hitler’s Germany. MelvilleHouse, Apr 2011.