Docetaxel is extensively used for treating different types of cancer; however, its clinical efficacy is primarily limited by myelotoxicity and peripheral neuropathy, adverse effects that often lead to treatment discontinuation. This study aimed to establish a preclinical model in Wistar rats for the simultaneous induction of myelotoxicity and peripheral neuropathy associated with docetaxel administration, enabling the evaluation of potential chemopreventive agents. Four distinct docetaxel administration schemes were assessed by performing behavioral nociceptive tests and complete blood cell counts. After establishing the damage model (5 mg/kg/week docetaxel for six weeks), we co-administered 100 mg/kg/week oral dimethyl fumarate to assess its protective effect. Dimethyl fumarate attenuated docetaxel-induced hyperalgesia, likely through preserving normal nerve fiber density in sciatic nerves, but neutropenia was not significantly mitigated. An alternative regimen with additional pre-administered doses of dimethyl fumarate showed a trend toward neutropenia attenuation and suggested an interesting inhibition of docetaxel-induced rat vibrissae loss. Chou-Talalay isobolographic analyses on prostate cancer cell lines revealed that dimethyl fumarate does not impair the therapeutic effect of docetaxel at most combination ratios evaluated; rather, synergistic effects were observed. This experimental model proved useful and will facilitate further research into the protective role of dimethyl fumarate and other potential chemoprotective agents.