We present a model for the Type Ia supernova remnant (SNR) of SN 1604, also known as Kepler's SNR. We find that its main features can be explained by a progenitor model of a symbiotic binary consisting of a white dwarf and an AGB donor star with an initial mass of 4-5 M_sun. The slow, nitrogen rich wind emanating from the donor star has partially been accreted by the white dwarf, but has also created a circumstellar bubble. Based on observational evidence, we assume that the system moves with a velocity of 250 km/s. Due to the systemic motion the interaction between the wind and the interstellar medium has resulted in the formation of a bow shock, which can explain the presence of a one-sided, nitrogen rich shell. We present two-dimensional hydrodynamical simulations of both the shell formation and the SNR evolution. The SNR simulations show good agreement with the observed kinematic and morphological properties of Kepler's SNR. Specifically, the model reproduces the observed expansion parameters (m=V/(R/t)) of m=0.35 in the north and m=0.6 in the south of Kepler's SNR. We discuss the variations among our hydrodynamical simulations in light of the observations, and show that part of the blast wave may have traversed through the one-sided shell completely. The simulations suggest a distance to Kepler's SNR of 6 kpc, or otherwise require that SN 1604 was a sub-energetic Type Ia explosion. Finally, we discuss the possible implications of our model for Type Ia supernovae and their remnants in general.