Context: A planetary nebula (PN) candidate was discovered during FORS imaging of the Local Group dwarf galaxy Phoenix. Aims: We use this PN to complement abundances from red-giant stars. Methods: FORS spectroscopy was used to confirm the PN classification. Empirical methods and photoionization modeling were used to derive elemental abundances from the emission line fluxes and to characterize the central star. Results: For the elements deemed most reliable for measuring the metallicity of the interstellar medium (ISM) from which the PN formed, [O/H] ~ -0.46 and [Ar/H] ~ -1.03. [O/H] has lower measurement errors but greater uncertainties due to the unresolved issue of oxygen enrichment in the PN precursor star. Conclusions: Earlier than 2 Gyr ago (the lower limit of the derived age for the central star) the ISM had Z = 0.002-0.008, a range slightly more metal-rich than the one provided by stars. Comparing our PN-to-stellar values to surveys of other dwarf Local Group galaxies, Phoenix appears to be an outlier.