The plant cannabinoids (phytocannabinoids), cannabidiol (CBD), and Δ⁹-tetrahydrocannabinol (THC) were previously shown to activate transient receptor potential channels of both vanilloid type 1 (TRPV1) and ankyrin type 1 (TRPA1), respectively. Furthermore, the endocannabinoid anandamide is known to activate TRPV1 and was recently found to antagonize the menthol- and icilin-sensitive transient receptor potential channels of melastatin type 8 (TRPM8). In this study, we investigated the effects of six phytocannabinoids [i.e., CBD, THC, CBD acid, THC acid, cannabichromene (CBC), and cannabigerol (CBG)] on TRPA1- and TRPM8-mediated increase in intracellular Ca²⁺ in either HEK-293 cells overexpressing the two channels or rat dorsal root ganglia (DRG) sensory neurons. All of the compounds tested induced TRPA1-mediated Ca²⁺ elevation in HEK-293 cells with efficacy comparable with that of mustard oil isothiocyanates (MO), the most potent being CBC (EC₅₀ = 60 nM) and the least potent being CBG and CBD acid (EC₅₀ = 3.4–12.0 μM). CBC also activated MO-sensitive DRG neurons, although with lower potency (EC₅₀ = 34.3 μM). Furthermore, although none of the compounds tested activated TRPM8-mediated Ca²⁺ elevation in HEK-293 cells, they all, with the exception of CBC, antagonized this response when it was induced by either menthol or icilin. CBD, CBG, THC, and THC acid were equipotent (IC₅₀ = 70–160 nM), whereas CBD acid was the least potent compound (IC₅₀ = 0.9–1.6 μM). CBG inhibited Ca²⁺ elevation also in icilin-sensitive DRG neurons with potency (IC₅₀ = 4.5 μM) similar to that of anandamide (IC₅₀ = 10 μM). Our findings suggest that phytocannabinoids and cannabis extracts exert some of their pharmacological actions also by interacting with TRPA1 and TRPM8 channels, with potential implications for the treatment of pain and cancer.