Living systems routinely consume energy to achieve motility, often using intricate biomolecular machinery. In this work, we demonstrate that active biomolecular condensates enable the self-propulsion of micron-sized objects in otherwise homogeneous, isotropic, and autonomous environments. Our proposed minimal mechanism consists of phase-separating proteins, enzymes passivating them, and complementary enzymes isotropically anchored to a spherical-colloid surface that reactivate the proteins. This passivation-activation cycle gives rise to a symmetry breaking wherein a single biocondensate is stabilized near the colloid surface, which in turn exerts a repulsive force on the colloid. We numerically demonstrate that this mechanism can propel micron-sized colloids at speeds of up to a hundred microns per second. This propulsion mode is strongly resistant to Brownian fluctuations and external forces. Propulsion mechanisms based on biomolecular condensates may thus offer a complementary, motor-free route to biological transport.