CONTEXT: Until now, only one planetary nebula (PN) has been known in the Fornax dwarf spheroidal galaxy. AIMS: The discovery of a second PN candidate, associated with one of the 5 globular clusters in the Fornax dwarf, is reported. METHODS: Spectra of the globular cluster H5, obtained with the UVES echelle spectrograph on the ESO Very Large Telescope, show [O III] line emission at a radial velocity consistent with membership of the Fornax dwarf. A possible counterpart of the [O III] emission is identified in archival images from the Wide Field Planetary Camera 2 on board the Hubble Space Telescope. The source of the emission is located about 1.5 (less than one core radius) southwest of the centre of the cluster. RESULTS: The emission line source is identified as a likely PN, albeit with several peculiar properties. No Hbeta, He I, or He II line emission is detected and the [O III]/Hbeta ratio is >25 (2 sigma). The expansion velocity inferred from the [O III] 5007 AA line is about 55 km/s, which is large for a PN. The diameter measured on the HST images is about 0.23 or 0.15 pc at the distance of the Fornax dSph. CONCLUSIONS: This object doubles the number of known PNe in Fornax, and is only the 5th PN associated with an old GC for which direct imaging is available. It may be a member of the rare class of extremely H-deficient PNe, the second such case found in a GC.