We study the temporal evolution of the circuit complexity for a subsystem in harmonic lattices after a global quantum quench of the mass parameter, choosing the initial reduced density matrix as the reference state. Upper and lower bounds are derived for the temporal evolution of the complexity for the entire system. The subsystem complexity is evaluated by employing the Fisher information geometry for the covariance matrices. We discuss numerical results for the temporal evolutions of the subsystem complexity for a block of consecutive sites in harmonic chains with either periodic or Dirichlet boundary conditions, comparing them with the temporal evolutions of the entanglement entropy. For infinite harmonic chains, the asymptotic value of the subsystem complexity is studied through the generalised Gibbs ensemble.
