Mycotoxins are secondary metabolites produced by various fungi. A very important category of mycotoxins are aflatoxins, considered to be the most dangerous in humans. Aflatoxin B1, well known as a favorable factor in the occurrence of hepatocellular carcinoma in humans, is the most controversial of all mycotoxins. Aflatoxins, found in naturally contaminated food, are resistant to degradation by heat. Current food processing practices and conventional storage conditions do not completely eliminate aflatoxin contamination from the food supply chain. Long storage food products—such as peanuts, pistachio, nuts in general, and dried fruits—are susceptible to aflatoxins contamination. The type of plastic material can influence the concentration of aflatoxins during storage due to the permeability to gas and moisture exchange with the external milieu. Nuts in general and dried fruits are consumed in large quantities worldwide. Therefore, herein we investigated the effect of plastic material on the total aflatoxins and aflatoxin B1 content in 64 samples of nuts and dried fruits packed and stored in low-density polyethylene (LDPE), polypropylene (PP), polyethylene (PE), and polyethylene terephthalate (PET). The method consisted in a cleanup procedure using immunoaffinity columns coupled with RIDASCREEN FAST immunoenzymatic competitive assays based on the ELISA technique. Collected data were subjected to statistical analysis and multiple comparisons tests were applied. From the total analyzed samples, 14.06% exceeded the maximum admitted European levels for total aflatoxins. The highest concentrations of total aflatoxins were obtained from samples packed in LDPE, followed by PP, PE, and PET. Aflatoxin B1 was detected in all samples packed in LDPE, PP, and PE. Most of the samples packed in PET had concentrations <1 µg/kg. These results indicate that nuts in general packed and stored in LDPE are more prone to contamination with aflatoxins, while PET is more suitable for maintaining the quality and safety of these products.