Resting-state functional magnetic resonance imaging (rs-fMRI) enables the evaluation of the language network and is particularly useful for measuring language lateralization with minimal participant effort and methodological biases (e.g., no language task execution or selection). Tractography using diffusion MRI (dMRI) provides complementary information on language-associated white matter bundles. Some structural white matter measures of the left or right hemisphere have been related to the functional language lateralization index (LI) and allow a better understanding of this network. This study utilizes tractography to identify white matter structural predictors of LI from a single hemisphere, employing linear regression and random forest models. Rs-fMRI and dMRI data from 618 healthy subjects of the Human Connectome Project were used to link LI to micro- and macro-structural measures of the arcuate fasciculi, the inferior longitudinal fasciculi, the frontal aslant tracts and sections of the corpus callosum. Results suggest a possible relationship between micro- and macro-structural measures of white matter tracts, and functional language lateralization measured in resting-state. However, the identified predictors are not sufficiently representative to be considered proxies for functional language lateralization. In conclusion, both micro- and macro-structural white matter characteristics as well as both left and right hemispheres are important to consider, but are not sufficient on their own, when investigating the relationship between brain structures and functional language lateralization.