Yes.

Germany did indeed have a community of approximately 20.-25.000 Afro-Germans. I have written about them here Many of them were from Germany's former colonies in Africa and the most well known group among them were the so-called Rhineland Bastards, children of black French Soldiers who had been stationed in the Rhineland. Many members of the latter group were not send to Concentration Camps but forcibly sterilized by the Nazis. As I have also written in the previous post linked above, Nazi Germany never formulated a coherent policy aside the general discrimination against on what was to happen with their Afro-German community, so they were not sent to Concentration Camps wholesale. There was however, a group of about 5.-6.000 North African Jews deported to Auschwitz in 1943. Unfortunately, we know very little about them because we have little in the ways of survivor testimony.

As for other examples of people of African descend in Concentration Camps, there were a number of members of the French and Belgian resistance arrested and deported to camps. The most known example of this is probably Jean Voste, a member of the Belgian resistance originally from the Congo. He is known as "the only black prisoner in Dachau". Here is a photograph that presumably shows him after liberation.

Another well-known example of an Afro-German imprisoned in a Concentration Camp was Bayume Mohamed Husen. Husen was a Tanzanian fighter in the German Colonial forces during German colonial rule. Able to migrate to Germany in 1929 he was an outspoken activist for a German Neo-Colonial movement. He also was a part of the Deutsch Afrika Schau, a colonialist spectacle comparable to a human zoo during National Socialism as well as pretty much taking on any film role that required a black person in the Third Reich. In 1941 he was arrested by Gestapo on charges of "racial defilement" (apparently he had cheated on his German wife with another German woman), was imprisoned in Sachsenhausen and was murdered there in 1944.

The history of the Asian community in Nazi Germany is less well researched than the history of the Afro-German community. The only significant Asian community in Germany I have come across is the Chinese. In 1935 there were about 1.500 to 1.800 Chinese people in Germany, most of them living in Hamburg and Berlin having been sailors and settling down there. The Chinese in Germany were faced with several discriminatory measure, especially since many had ties to leftism and some had even served with the Republicans in Spain.

In 1938, the Reich Security Main Office (RSHA) under Reinhard Heydrich instituted the Zentralstelle für Chinese, a bureau with the specific task of preventing Chinese immigration to Germany and controlling those Chinese who lived there. In Berlin, the members of this RSHA bureau interned all the Chinese living there in Arbeitserziehungslager Langer Morgen. Arbeitserziehungslager were not Concentration Camps in that they were not run by the WVHA but instead by the local Gestapo. These camps were smaller but the living conditions there were not significantly less brutal than in the Concentration Camps.

In Hamburg, in May 1944 the Gestapo raided the part of town to which the Chinese living there had been forcibly confined in 1942. The so-called "Chinesenaktion" resulted in an additionally 130 Chinese being sent to Langer Morgen, where some of them such as Chan Ho Bau and Liang Wong were murdered.

Another and often forgotten example of racially motivated murder by the Nazi against East Asians is the treatment of East Asian and specifically Mongol Soviet soldiers. Together with Jewish POWs and Bolshevik Commissars, they belonged to the group of Soviet POWs who were singled out specifically to be killed by the Einsatzgruppen. The Mongols as the embodied of the "Asiatic Horde" in Nazi racial delusions were seen as especially dangerorus too. Where they weren't killed immediately, they often found themselves deported to the larger Concentration Camps such as Auschwitz to be killed there. The exact number is not known but it is important to include them in the racial victims of the Nazi regime.

Sources:

Additionally to the sources I have in the linked comment above, also see:

• Lars Amenda: „Chinesenaktion“: Zur Rassenpolitik und Verfolgung im nationalsozialistischen Hamburg. In: Zeitschrift des Vereins für Hamburgische Geschichte. Band 91, 2005, S. 103–132.

• Lars Amenda: Fremde, Hafen, Stadt. Chinesische Migration und ihre Wahrnehmung in Hamburg 1897–1972 (= Forum Zeitgeschichte. Bd. 17). Dölling und Galitz, München u. a. 2006.

• Bechhaus-Gerst, Marianne (2007). Treu bis in den Tod: von Deutsch-Ostafrika nach Sachsenhausen. Eine Lebensgeschichte. Berlin.

• Herbert Diercks: Der Hamburger Hafen im Nationalsozialismus. Wirtschaft, Zwangsarbeit und Widerstand; herausgegeben von der KZ-Gedenkstätte Neuengamme, Hamburg 2008.

• Benton, Gregor (2007), "Germany", Chinese Migrants and Internationalism, Routledge, S. 30–37.

• Gütinger, Erich (1998), "A Sketch of the Chinese Community in Germany: Past and Present", in The Chinese in Europe von Benton, Gregor; Pieke, Frank N., Macmillan, S.199–210.

• For Nazi racial policy and the Mongols: Richard Breitman: Hitler and Genghis Khan. In: Journal of Contemporary History, Vol. 25, No. 2/3 (May - Jun., 1990), pp. 337-351.