Nobody knows for sure what race Noah belong to. But right after the flood, his family migrated from Ararat to southern Mesopotamia and established the first city... Babel. Right after a failed construction of the tower, they spawned the races we know of today. Here's a list of Noah's children and their descendants, and the races (or Y-DNA Haplogroups) they were when the great migration started:
Noah's son Shem
Semitic Race, Haplogroup J
Noah's son Ham's son Canaan
Australoid Race, Haplogroup C
Ham's son Cush
Black Race
Ham's son Mizraim
Pygmy Race, Haplogroup B
Ham's son Phut
Atlanto-Mediterranean Race, Haplogroup E3b
Noah's son Japheth's son Gomer
Brunn Race, Haplogroup R1b
Japheth's son Tiras
Nordic Race, Haplogroup I
Japheth's son Magog
Mongoloid Race, haplogroups N & O
Japheth's son Tubal
Dinaric Race
Japheth's son Meshech
Alpine Race, Haplogroup G
Japheth's son Madai
Irano-Afghan Race, Haplogroup R1a
Japheth's son Javan
Eastern Mediterranean Race, Haplogroup K