We consider the problem of approximate calculation of quantum mutual information in a bipartite quantum state where one of subsystems goes through a decoherence process (quantum channel). The approximation employs a reduced density matrix of the subsystem affected by decoherence and the initial value of mutual information before decoherence. We test the approximation on sets of randomly generated qubit-qudit mixed states for three types of qubit decoherence channels: dephasing, depolarizing, and damping. We consider how approximation accuracy is related to decoherence type, decoherence strength, and the dimension of the qudit subsystem.