Muon spin rotation (μSR) experiments were performed on the intercalated graphite CaC₆ in the normal and superconducting state down to 20 mK. In addition, AC magnetization measurements were carried out resulting in an anisotropic upper critical field H_c2, from which the coherence lengths ξ_ab(0) = 36.3(1.5) nm and ξ_c(0) = 4.3(7) nm were estimated. The anisotropy parameter γ_H = H^ab_c2/H^c_c2 increases monotonically with decreasing temperature. A single isotropic s-wave description of superconductivity cannot account for this behavior. From magnetic field dependent μSR experiments, the absolute value of the in-plane magnetic penetration depth λ_ab(0) = 78(3) nm was determined. The temperature dependence of the superfluid density ρ_s(T) is slightly better described by a two-gap than a single-gap model.