I never used MRIcro for that purpose but it seems quite quick in SPM.
Use [Y,XYZ]=spm_read_vols(spm_vol(spm_get)) specifying binary mask as input
to get voxel values in Y.
Then use length(find(Y)) to get the number of non-zero voxels.
that number over voxel size will be the volume in mm3