The magnetic penetration depth anisotropy gamma(lambda) = lambda(c)/lambda(ab) (lambda(ab) and lambda(c) are the in-plane and the out-of-plane components of the magnetic penetration depth) in a CaKFe4As4 single crystal sample (the critical temperature T-c similar or equal to 35 K) was studied by means of muon-spin rotation (mu SR). gamma(lambda) is almost temperature independent for T less than or similar to 20 K (gamma(lambda) similar or equal to 1.9) and it reaches similar or equal to 3.0 by approaching T-c. The change of gamma(lambda) induces the corresponding rearrangement of the flux line lattice (FLL), which is clearly detected via enhanced distortions of the FLL mu SR response. A comparison of gamma(lambda) with the anisotropy of the upper critical field (gamma H-c2) studied by Meier et al. [Phys. Rev. B 94, 064501 (2016)] reveals that gamma(lambda) is systematically higher than gamma H(c2 )at low temperatures and approaches gamma H-c2 for T -> T-c. The anisotropic properties of lambda are explained by the multigap nature of superconductivity in CaKFe4As4 and are caused by anisotropic contributions of various bands to the in-plane and the out-of-plane components of the superfluid density.