In this work, ceramic monolithic catalyst carriers based on zirconium dioxide (ZrO2) were prepared by fused filament fabrication. The active catalyst components were deposited on the obtained supports by the wet impregnation technique. The activity of the prepared catalysts was tested by carrying out the catalytic oxidation of a mixture of aromatic compounds, including benzene, toluene, ethylbenzene, and o-xylene (BTEX). The efficiency of the prepared monolithic catalysts used for the catalytic oxidation of BTEX was determined with respect to the chemical composition of the catalytically active component (MnFeOx, MnCuOx, and MnNiOx) and with respect to the geometry of the monolithic carrier (ZDP, Z, and M). Prior to the kinetic measurements, the dimensional stability of the 3D-printed monolithic carriers and the mechanical stability of the catalyst layer were investigated. Characterization of the ZrO2 filament used was performed too. X-ray diffraction analysis showed that the ceramic phase of the material consists of monoclinic and tetragonal ZrO2. The size of the ceramic particles was determined by laser diffraction analysis. The results of the analysis showed that the size of the ceramic particles ranged from 71 to 3000 μm. The median value of the particle size (d50) in the population was 540.10 μm. The predominant size of the ceramic particles in the population (dmode) was 562.34 μm, and the Sauter diameter (d3,2) of the particles was 886.25 μm. The thermal properties of the ZrO2 filament used to prepare monolithic carriers were investigated by simultaneous TGA/DTA analysis. The dimensional correction factor was determined by measuring the characteristic dimensions of the 3D-printed monolithic carriers against the dimensions predicted by the CAD model. The value of the dimensional correction factor was 1.18. Based on the measured mass deviation of the 3D-printed carriers, a uniform distribution of the ceramic particles in the printed carriers was observed. The mechanical stability of the catalytic layer was determined by adhesion tests. The catalyst was exposed to ultrasound at a frequency of 37 kHz. The loss of the catalytic layer due to the ultrasonic vibrations was from 0.016% to 0.051%, proving the excellent mechanical stability of the prepared catalytic layers. The results of the efficiency of the prepared monolithic catalysts used for the catalytic oxidation of BTEX showed that the 3D-printed model M, which contained MnFeOx as the catalytically active component, was the most successful catalyst for the oxidation of BTEX compounds. The mentioned catalyst enables catalytic oxidation of all components of the BTEX mixture at a temperature of 177 °C.