Here’s a short (not extensive) overview of international supermarkets in Cologne:

General African Asian & Afroshop Lebensmittel (im Kwartier Latäng), Afro Shop (in Ehrenfeld)
Arabic Acima (in Kalk), Bilad Al Sham (in Mülheim)
General (South/East) Asian Heng Long Asia Supermarkt (in Lindenthal), Ho's Supermarket (am Eigelstein), Asia Markt Wing on Hong (in Raderberg), Seng Heng (im Kwartier Latäng), Go Asia (in der Innenstadt)
Australian Australia Shopping World (im Belgischen Viertel)
Brazilian Asian & Afroshop Lebensmittel - you’ll also find Brazilian items (im Kwartier Latäng)
Indian Asien Bazar indische Spezialitäten (am Neumarkt), Tropical Fruits (am Neumarkt)
Iranian Bazarche Sharghi (in Sülz), Multi Kulti Bazar Diba (in Nippes)
Italian Andronaco (in Ossendorf), Mare Atlantico (in Raderberg), Nadia (in Mülheim)
Korean Hana Korea Shop (in Zollstock), Seoulshop (in Sülz)
General Latin America Hola Mundo (im Kwartier Latäng), Doña Pelos (im Agnesviertel)
Moroccan Tanger (in Neustadt-Süd), Saharashop (in Kalk)
Mexican Doña Pelos (im Agnesviertel), Seng Heng - mainly Asian but also with Mexican items (im Kwartier Latäng)
Polish Sobieski Supermarkt (in Kalk)
Russian Mix Markt (in Holweide), Zabawa (in Buchheim)
Spanish Anduronda (in Raderberg), Solera (in Ossendorf)
Turkish Karadag Supermarkt (am Eigelstein, in Ehrenfeld, in Nippes and in Mülheim),  SOK Supermarkt (in Ehrenfeld, in Mülheim and in Nippes)