Most runaway OB stars, like the majority of massive stars residing in their parent clusters, go through the red supergiant (RSG) phase during their lifetimes. Nonetheless, although many dozens of massive runaways were found to be associated with bow shocks, only two RSG bow-shock-producing stars, Betelgeuse and μ Cep, are known to date. In this paper, we report the discovery of an arc-like nebula around the late M-type star IRC –10414 using the SuperCOSMOS H-alpha Survey. Our spectroscopic follow-up of IRC –10414 with the Southern African Large Telescope (SALT) showed that it is a M7 supergiant, which supports previous claims on the RSG nature of this star based on observations of its maser emission. This was reinforced by our new radio- and (sub)millimetre-wavelength molecular line observations made with the Atacama Pathfinder Experiment 12-m telescope and the Effelsberg 100-m radio telescope, respectively. The SALT spectrum of the nebula indicates that its emission is the result of shock excitation. This finding along with the arc-like shape of the nebula and an estimate of the space velocity of IRC –10414 (70 ± 20 km s –1 ) imply the bow shock interpretation for the nebula. Thus, IRC –10414 represents the third case of a bow-shock-producing RSG and the first one with a bow shock visible at optical wavelengths. We discuss the smooth appearance of the bow shocks around IRC –10414 and Betelgeuse and propose that one of the necessary conditions for stability of bow shocks generated by RSGs is the ionization of the stellar wind. Possible ionization sources of the wind of IRC –10414 are proposed and discussed.