Unable to pursue his career, Schwab emigrated from Nazi Germany to Greece in 1939, He and Elly married in Athens in the same year. With the connections of his wife, both started research work in the industrial chemistry laboratory of the recently founded Kanellopoulos Institute of Chemistry and Agriculture in Piraeus.
For the following years he spent in Greece, Schwab (known in Greek as Γεώργιος Σβαμπ, ) came to view Greece as "his second fatherland".
While in the Kanellopoulos Institute, a sui generis research institution for contemporary Greece, he was allowed to pursue purely scientific work; indeed Schwab had a fruitful 11-year stay marked by a series of incidental discoveries as well as systematic studies continuing his previous work on catalysis.
Schwab was in a difficult situation during the Axis occupation of Greece, when he once again faced danger from the German occupying forces due to his Jewish background. In 1942, the German authorities refused to renew his German passport. Georg-Maria escaped the fate of his brother, Josef-Maria Schwab – who died as a forced labourer in Organisation Todt, by keeping a low profile in Greece and getting an exemption from the 1943 order for German citizens to return to Germany with the help of an official at the German Embassy in Athens.
After the liberation of Greece (1944), Schwab was able to resume his research at the Kanellopoulos Institute, until he was offered the Professorship of Physical Chemistry at the Technical University of Athens in 1949. He kept the position and taught the subject for the next 10 years.