We report the discovery of a planetary nebula centered on the poorly studied symbiotic binary star DT Ser. In a few other symbiotic stars spatially resolved nebulae have been discovered as well, but only one of them probably is a genuine planetary nebula, while the others are likely to originate in complex mass-ejection episodes from the interacting binary central stars that are possibly related to nova-like outbursts. The rim of the planetary nebula around DT Ser is severely distorted toward a brighter star 5 arcsec away. In infrared WISE data, this star shows the presence of a detached cold-dust shell similar to those observed in post-AGB stars. The apparent association of the symbiotic star and its planetary nebula with the nearby possible post-AGB object is discussed. We also discuss the sparse and conflicting literature data that could support an observed variability of the surface brightness of the planetary nebula. The puzzling and intriguing characteristics displayed by DT Ser are surely worth additional and more detailed investigations.