Currently, bone age is assessed by X-rays. It enables the evaluation of the child’s development and is an important diagnostic factor. However, it is not sufficient to diagnose a specific disease because the diagnoses and prognoses may arise depending on how much the given case differs from the norms of bone age. Background: The use of magnetic resonance images (MRI) to assess the age of the patient would extend diagnostic possibilities. The bone age test could then become a routine screening test. Changing the method of determining the bone age would also prevent the patient from taking a dose of ionizing radiation, making the test less invasive. Methods: The regions of interest containing the wrist area and the epiphyses of the radius are marked on the magnetic resonance imaging of the non-dominant hand of boys aged 9 to 17 years. Textural features are computed for these regions, as it is assumed that the texture of the wrist image contains information about bone age. Results: The regression analysis revealed that there is a high correlation between the bone age of a patient and the MRI-derived textural features derived from MRI. For DICOM T1-weighted data, the best scores reached 0.94 R2, 0.46 RMSE, 0.21 MSE, and 0.33 MAE. Conclusions: The experiments performed have shown that using the MRI images gives reliable results in the assessment of bone age while not exposing the patient to ionizing radiation.