The effect of intrinsic channel noise is investigated for the dynamic response of a neuronal cell with a delayed feedback loop. The loop is based on the so-called autapse phenomenon in which dendrites establish connections not only to neighboring cells but also to its own axon. The biophysical modeling is achieved in terms of a stochastic Hodgkin-Huxley model containing such a built in delayed feedback. The fluctuations stem from intrinsic channel noise, being caused by the stochastic nature of the gating dynamics of ion channels. The influence of the delayed stimulus is systematically analyzed with respect to the coupling parameter and the delay time in terms of the interspike interval histograms and the average interspike interval. The delayed feedback manifests itself in the occurrence of bursting and a rich multimodal interspike interval distribution, exhibiting a delay-induced reduction in the spontaneous spiking activity at characteristic frequencies. Moreover, a specific frequency-locking mechanism is detected for the mean interspike interval.