Antimicrobial low‐density polyethylene (LDPE) films were developed by adding 0%, 0.5%, 1.0%, 2.5% and 5.0% (w/w) of Mexican oregano essential oil (OEO) or potassium sorbate (PS) as a positive antifungal control to inhibit the growth of Penicillium expansum, Penicillium citrinum and Aspergillus niger in vitro. Three methods of adding OEO in LDPE were evaluated; the best OEO yield in film was achieved when OEO was incorporated after laminating (88%); otherwise, when added into cool‐melting resin, OEO lost up to 91.5% from LDPE and completely volatilized (>99%) when combined with the resin before melting. PS yields in LDPE film were > 88% when incorporated into cool‐melted resin. Antimicrobial films with 2.5% or 5.0% (w/w) OEO or PS delayed the growth of P. expansum and P. citrinum for up to 4–5 days, and for A. niger, only films with 5.0% of OEO retarded its growth for 5 days. The modified Gompertz model was used to describe mould growth response, obtaining the parameters A (maximum growth), μm (maximum growth rate) and λ (lag phase), which correctly fit the data. P. citrinum was the most sensitive mould, and A. niger was the most resistant to the tested antimicrobials. The addition of antimicrobial agents significantly (p < 0.05) impacted the physical and mechanical properties of the LDPE films, wherein thickness and puncture strength were increased, and the colour changed (reducing the transparency and promoting the yellowness). In contrast, the water vapour transmission rate was dropped only by incorporating PS.