An efficient method for the detection of acetone, an important biomarker in exhaled breath, by utilizing wavelength modulation spectroscopy (WMS) with a mid-infrared distributed feedback interband cascade laser (DFB-ICL) is presented. The performance of the DFB-ICL laser is characterized, and its linewidth is measured to be $\mbox{(3}.\mbox{39} \pm 0.\mbox{15)}$(3.39±0.15) MHz by beating the output with an auxiliary mid-IR frequency comb over 50 ms. The measured asymmetric acetone absorption profile with the center wavelength around 3367 nm is fitted by the pseudo-Voigt function. The phase shift between the intensity and frequency modulations is determined and used for processing the results. The sensor is tested by performing measurements with calibration mixtures of acetone in nitrogen, and the detection limits of 0.58 ppm and 0.12 ppm were determined with 1 s and 60 s signal averaging times, respectively. Our work shows that wavelength modulation spectroscopy with a DFB-ICL laser complimented by a multipass cell for higher sensitivity can be efficiently used for acetone detection and is promising for sensitive breath analysis.