I am afraid you can not calculate carbon storage of a specific vegetation cover without further research on establishing a statistical model to relate ndvi values to your vegetation of interest. You may got lucky and find a similar work that established statistical models. Then you can use the model to convert ndvi values to carbon storage.
your NDVI values are generally related to primary productivity. A lot depends on the time-scale of your specific application. As a starting point, refer to, e.g. this paper that related NET primary production (NPP) to NDVI
Field, C.B.; Behrenfeld, M.J., Randerson, J.T. and Falkowski, P. (1998). "Primary production of the Biosphere: Integrating Terrestrial and Oceanic Components". Science 281 (5374):
Keep in mind you will also need temperature and radiation as model inputs.