Many evolution partial differential equations (PDEs) can be cast into Hamiltonian form. Conservation laws of these equations are related to one-parameter Hamiltonian symmetries admitted by the PDEs [P. J. Olver, Applications of Lie Groups to Differential Equations (Springer, New York, 1986)]. In this paper we consider symmetries and Noether’s theorem for semidiscrete Hamiltonian equations which are obtained by space discretization of Hamiltonian PDEs. Using symmetries, one can find conservation laws of these equations. Several applications including a transfer equation and the Korteweg–de Vries equation are presented.