Context : Ultra-compact dwarfs ( UCDs ) are stellar systems displaying colours and metallicities between those of globular clusters ( GCs ) and early-type dwarf galaxies , as well as sizes of R _ { eff } \lesssim 100 pc and luminosities in the range -13.5 < M _ { V } < -11 mag . Although their origin is still subject of debate , the most popular scenarios suggest that they are massive star clusters or the nuclei of tidally stripped dwarf galaxies . Aims : NGC 5044 is the central massive elliptical galaxy of the NGC 5044 group . Its GC/UCD system is completely unexplored . Methods : In Gemini+GMOS deep images of several fields around NGC 5044 and in spectroscopic multi-object data of one of these fields , we detected an unresolved source with g ^ { \prime } \sim 20.6 mag , compatible with being an UCD . Its radial velocity was obtained with FXCOR and the penalized pixel-fitting ( pPXF ) code . To study its stellar population content , we measured the Lick/IDS indices and compared them with predictions of single stellar population models , and we used the full spectral fitting technique . Results : The spectroscopic analysis of the UCD revealed a radial velocity that agrees with the velocity of the elliptical galaxy NGC 5044 . From the Lick/IDS indices , we have obtained a luminosity-weighted age and metallicity of 11.7 ^ { +1.4 } _ { -1.2 } Gyr and [ Z / H ] = -0.79 \pm 0.04 dex , respectively , as well as [ \alpha / Fe ] = 0.30 \pm 0.06 . From the full spectral fitting technique , we measured a lower age ( 8.52 Gyr ) and a similar total metallicity ( [ Z / H ] = -0.86 dex ) . Conclusions : Our results indicate that NGC 5044-UCD1 is most likely an extreme GC ( M _ { V } \sim - 12.5 mag ) belonging to the GC system of the elliptical galaxy NGC 5044 .