At an early age, hydration of cement leads to a reduction in volume (caused by Le Chatelier contraction) that induces autogenous shrinkage. In addition, hydration is an exothermic reaction, and an increase in temperature occurs (followed by a decrease). Because autogenous shrinkage arises only in cement paste, and because the coefficient of thermal expansion may be different between cement paste and aggregates, strain incompatibilities lead to an internal self-equilibrated state of stress. Depending especially on the concrete mix, initial cracking may occur at the cement-paste scale leading to a modification of the global concrete behavior. In this paper, finite-element simulations using a mesoscopic mesh are performed to access to the internal stresses and damage state resulting from the hydration process. Calculations take into account the autogenous shrinkage of the cement paste and the differential thermal behavior between cement paste and aggregates. The influences of basic creep strains, thermal boundary conditions, and concrete mix (by a simplified approach) are studied, and it is shown that for ordinary concrete, hydration leads to a slight reduction in elastic stiffness and tensile strength when creep is taken into account. However, for high-performance concrete, a significant reduction in the elastic stiffness and tensile strength is expected (with respect to the potential tensile strength) even if creep is taken into account.