Osteoporosis is characterized by decrease of bone mineral density and alterations of the bone microarchitecture, leading to bone fragility and an increased risk of fractures. Discrimination between osteoporotic and healthy subjects using X-ray images presents a major challenge for medical image analysis and classification. This work introduces a new approach based on multifractal texture analysis for the characterization of the trabecular bone microarchitecture to distinguish between Control Subjects (CS) and Osteoporotic Patients (OP). The proposed method enables a description of both local and global regularity and roughness of the trabecular bone on radiographic images. To this end, the multifractal spectrum is exploited to extract new texture attributes and reveal bone microarchitecture changes due to osteoporosis. To assess the proposed approach effectiveness, tests were carried out for the classification of two populations (CS and OP) using a logistic regression model. A classification rate of 98.01% was reached showing that the proposed approach presents a promising potential as a complementary tool for osteoporosis diagnosis.