Yes. He deemed it Degenerate Art. In 1937, the Third Reich collected as much as possible (by collected, I mean stole, pillaged, etc.) and then (without the information in front of me, I believe it was the Goebbels acting as Minister of Propaganda among others who) created an exhibition of the work called the Degenerate Art Exhibition. This exhibition toured Germany for just under 5 months and included many very important works of art including works by Picasso, Kandinsky, Chagall, Mondrian, Klee, etc.

The whole exhibit was arranged specifically to denigrate the works. Some were hung on their side, some upside-down. The rooms were organized into themes, such as madness, the jew (and negro) as degenerates, sabatoge of the german nation, etc. It was not at all a positive show. Though there was a very high turnout for these exhibitions (particularly in Berlin), it is generally believed that most the German people who went were going in order to see these works before they were destroyed.

Throughout the reign of the Third Reich, there was no support for modern artists. They were fired from their academic positions, were called into court for treasonous charges, and many fled to the United States (which helped push the USA into becoming a cultural frontrunner in art). Because of this mass exodus (at least in part), the style of Abstract Expressionism was able to evolve and develop into one of the most recognized and historically important are periods of the 20th C.

Sidenote: the USA purposefully supported Abstract Expressionism because it was a cultural opposition to the Nazis. While the Nazis were decrying it as a threat to the evolved human and perfect kultur that is Germany, the US was bolstering it as proof that they were more open minded and better than Germany.

Edit: I used the wrong 'there'.

I think and I know Goering did, many people collected art, exspecially modern one. Many paintings are lost, some were discovered, again. Last year was a big case, where art was discovered. A man lived with many paintings in his home (his dad was a collector in ww2) and he sold from time to time a painting for living, on the black market. Knowing about him an Goering makes me believe, that the Nazis didn't destroy that much. They sold it and many big people stole it. It's more complex, but I am not native english and have to do more research about it, too. I believe many paintings are still in private households and maybe the owner don't know about it or, if they know they will keep it or try to sell it illegal.