Using finite-difference time-domain simulations it is shown that a metal-insulator-metal (MIM) ring with a narrow gap exhibits plasmonic stop bands (PLSBs) in a similar way that a microstrip ring with a narrow gap exhibits photonic stop bands. A narrow gap created in the middle of the upper half of a regular MIM ring causes plasmonic fields to experience multiple reflections at the discontinuity introduced by the gap, which results in the formation of PLSBs. The PLSBs appear as transmission dips around the resonant frequencies of the isolated MIM ring with the narrow gap. The centre frequency and the range of PLSBs are shown to be controllable by varying the width of the narrow gap. The proposed design for a MIM ring in which PLSBs exist is expected to reduce the size of the plasmonic devices.