Background: Diffusion-weighted imaging and elastography are widely accepted methods in the evaluation of breast masses, however, there is very limited data comparing the two methods. The apparent diffusion coefficient is a measure of the diffusion of water molecules obtained by diffusion-weighted imaging as a part of breast MRI. Breast elastography is an adjunct to conventional ultrasonography, which provides a noninvasive evaluation of the stiffness of the lesion. Theoretically, increased tissue density and stiffness are related to each other. The purpose of this study is to compare MRI ADC values of the breast masses with quantitative elastography based on ultrasound shear wave measurements and to investigate their possible relation with the prognostic factors and molecular subtypes. Methods: We retrospectively evaluated histopathologically proven 147 breast lesions. The molecular classification of malignant lesions was made according to the prognostic factors. Shear wave elastography was measured in kiloPascal (kPa) units which is a quantitative measure of tissue stiffness. DWI was obtained using a 1.5-T MRI system. Results: ADC values were strongly inversely correlated with elasticity (r = −0.662, p < 0.01) according to Pearson Correlation. In our study, the cut-off value of ADC was 1.00 × 10−3 cm2/s to achieve a sensitivity of 84.6% and specificity of 75.4%, and the cut-off value of elasticity was 105.5 kPa to achieve the sensitivity of 96.3% and specificity 76.9% to discriminate between the malignant and benign breast lesions. The status of prognostic factors was not correlated with the ADC values and elasticity. Conclusions: Elasticity and ADC values are correlated. Both cannot predict the status of prognostic factors and differentiate between molecular subtypes.