UPDATE: IN S2E21, the Season 2 Finale, when specifically asked "is Nick a Wesen" Monroe and Rosalee immediately (and vehemently) explain that he is not, that he is human.
Based on the idea that Wesen are all distinct species (or perhaps sub-species), no, Grimms are not.
Grimms are all descended from human knights that participated in the Fourth Crusade, where they found a treasure that apparently needed protecting. Grimms are never referred to as Wesen, and all Wesen seem to group them into a "not us" category, so whatever Grimms are, they are not Wesen. However, they do appear to have some level of supernatural ability that normal humans do not have, including:
- The enhanced physical skills
- The ability to see Wesen even in disguise
- The ability to destroy the Wesen part of a Wesen, turning them human.
These abilities are also genetic, but do not manifest in every descendant of a Grimm. This means that "Grimm" is not a species, but rather a talent or trait, like red hair or good singing voice, that is passed on genetically from human to human. It appears that Wesen/human hybrids exist, so perhaps some Grimms are also part Wesen, but that is not the norm.
(Note that at least one Wesen has stated that a Grimm "couldn't be" a Wesen, but no explanation was given as to why.)