Abstract: Biexcitons in fractional dimensional spaces are studied using variational quantum Monte Carlo. We investigate the biexciton binding energy as a function of the electron-hole mass fraction sigma as well as study the dimensional dependence of biexcitons for sigma = 0 and sigma = 1. As our first application of this model we treat the H(2) molecule in two and three dimensions. Next we investigate biexcitons in carbon nanotubes within the fractional dimensional model. To this end we find a relation between the nanotube radius and the effective dimension. The results of both applications are compared with results obtained using different models and we find a reasonable agreement. Within the fractional dimensional model we find that the biexciton binding energy in carbon nanotubes accurately scales as E(B)(r,epsilon) = 1280 meV angstrom/(r epsilon), as a function of radius r and the dielectric screening epsilon.