The intrinsic plasticity or brittleness of crystalline metals correlates with the ratio of the elastic shear modulus μ to the bulk modulus B; when the ratio μ/B exceeds a critical value, the metal is brittle. Sufficient data on elastic moduli and toughness are now available to permit an assessment for metallic glasses. We find a similar correlation, with the critical value of μ/B for metallic glasses (0.41-0.43) more sharply defined than for crystalline metals. This critical value applies also for annealing-induced embrittlement of metallic glasses. The clear correlation between mechanical behaviour (plasticity or brittleness) and μ/B assists in understanding flow and fracture mechanisms, and in guiding alloy design to alleviate brittleness of metallic glasses.