Osteoporosis is a condition of fragile bone with an increased susceptibility to fracture. Since the gold standard method used for the diagnosis of osteoporosis, Dual X-ray Absorptiometry (DXA), is expensive and not widely available in low economies, there is a need for low cost approaches to detect bone loss in people. A new automated radiogrammetric method for early diagnosis of osteoporosis from a single hand radiograph is proposed. In this technique, the third metacarpal bone is segmented from hand X-ray images using Active Appearance Models (AAM). Points of interest acquired from the segmented bone are used to take radiogrammetric measurements, from which bone indices are calculated. Data used in this work was acquired from 138 subjects in two hospitals in India. Significant radiogrammetric features were selected using statistical analysis. The bone indices are observed to be significantly correlated with Bone Mineral Density (BMD) of the lumbar spine measured using DXA. Different classification models were trained using the significant features. The results obtained are promising and can be used as a cost effective diagnostic tool for early detection of osteoporosis.