Context. Observations of the supernova remnant (SNR) Cassiopeia A (Cas A) show significant asymmetries in the reverse shock that cannot be explained by models describing a remnant expanding through a spherically symmetric wind of the progenitor star. Aims. We investigate whether a past interaction of Cas A with a massive asymmetric shell of the circumstellar medium can account for the observed asymmetries of the reverse shock. Methods. We performed three-dimensional (3D) (magneto)-hydrodynamic simulations that describe the remnant evolution from the SN explosion to its interaction with a massive circumstellar shell. The initial conditions (soon after the shock breakout at the stellar surface) are provided by a 3D neutrino-driven SN model whose morphology closely resembles Cas A (Wongwathanarat et al. 2017). The SNR simulations cover ≈ 2000 years of evolution and include all physical processes necessary to describe the remnant-shell interaction. We explored the parameter space of the shell, searching for a set of parameters able to produce reverse shock asymmetries at the age of ≈ 350 years analogous to those observed in Cas A.Results. The interaction of the remnant with the shell can match the observed asymmetries in the reverse shock if the shell was asymmetric with the densest portion in the (blueshifted) nearside to the northwest (NW). According to our favorite model, the shell was thin (thickness σ ≈ 0.02 pc) with a radius r sh ≈ 1.5 pc from the center of the explosion. The reverse shock shows the following asymmetries at the age of Cas A: i) it moves inward in the observer frame in the NW region, while it moves outward in other regions; ii) the geometric center of the reverse shock is offset to the NW by ≈ 0.1 pc from the geometric center of the forward shock; iii) the reverse shock in the NW region has enhanced nonthermal emission because, there, the ejecta enter the reverse shock with a higher relative velocity (between 4000 and 7000 km s −1 ) than in other regions (below 2000 km s −1 ). Conclusions. The main asymmetries observed in the reverse shock of Cas A can be interpreted as signatures of the interaction of the remnant with an asymmetric dense circumstellar shell that occurred between ≈ 180 and ≈ 240 years after the SN event. We suggest that the shell was, most likely, the result of a massive eruption from the progenitor star that occurred about 10 5 years prior to core-collapse. We estimate a total mass of the shell of M sh ≈ 2.6 M ⊙ .