Nanocomposites of multiwalled carbon nanotubes (MWCNTs) with poly(butylene adipate-co-terephthalate) (PBAT), a flexible aromatic–aliphatic copolyester, were prepared by melt mixing followed by compression moulding to investigate their spectroscopic, morphological, mechanical and electrical properties. A comparison of the Fourier transform infrared (FTIR) spectra of the neat polymer matrix and the composites showed no difference, implying a physical mixing of the matrix and the filler. A morphological investigation revealed the formation of a continuous and interconnected MWCNT network embedded in the polymer matrix with partial agglomeration. Increasing Martens hardness and indentation modulus and decreasing maximum indentation depth with increasing filler concentration demonstrated the reinforcement of the polymer by the MWCNTs. A volume resistivity of 4.6 × 10⁵ Ω cm of the materials was achieved by the incorporation of only 1 wt.-% of the MWCNTs, which confirmed a quite low percolation threshold (below 1 wt.-%) of the nanocomposites. The electrical volume resistivity of the flexible nanocomposites was achieved up to 1.6 × 10² Ω cm, depending on the filler content. The elongation at the break of the nanocomposites at 374% and the maximum relative resistance changes (ΔR/R₀) of 20 and 200 at 0.9 and 7.5% strains, respectively, were recorded in the nanocomposites (3 wt.-% MWCNTs) within the estimated volume resistivity range. A cyclic strain experiment shows the most stable and reproducible ΔR/R₀ values in the 2%–5% strain range. The electrical conductivity and piezoresistivity of the investigated nanocomposites in correlation with the mechanical properties and observed morphology make them applicable for low-strain deformation-sensing.