We report the discovery of a low-mass transiting brown dwarf orbiting TOI-6884 (TIC 156514476, $T_{\rm mag}=11.4$) from NASA's Transiting Exoplanet Survey Satellite (TESS) mission. The TESS light curves initially suggested an orbital period of $\sim$14.42 d; however, our high-precision ground-based radial velocity measurements and multi-epoch time-series photometry reveal this to be a harmonic alias. We determine the true orbital period to be $4.808264^{+0.000015}_{-0.000014}$ d and confirm the substellar nature of the companion. TOI-6884b has a mass of $26.32^{+0.98}_{-0.93}$$\, M_{\rm J}$, a radius of $0.927^{+0.51}_{-0.52}$ $\, R_{\rm J}$, and resides on a nearly circular orbit ($e=0.067^{+0.010}_{-0.012}$). Its host star is a late F-type slightly evolved star with $M_\star = 1.410^{+0.075}_{-0.069}$ $\mathrm{ M}_\odot$, $R_\star = 1.840^{+0.072}_{-0.073}$ $\mathrm{ R}_\odot$, $\log {g} = 4.057^{+0.045}_{-0.039}$, $[{\rm Fe/H}] = 0.094^{+0.073}_{-0.068}$ dex, and $T_{\rm eff}=6330^{+180}_{-160}$ K. TOI-6884b is a key addition to the small population of well-characterized transiting brown dwarfs orbiting host stars that have left the main sequence. The detection of such systems will contribute to our understanding of dynamical histories and structural evolution of short-period substellar companions around evolved stars.