Magnetic skyrmions with a topological particle nature are considered as potential information carriers for future spintronics memory and logic devices. The stabilization of magnetic skyrmions at zero magnetic field in nanostructured components is a prerequisite for incorporating them into advanced nonvolatile memory devices. Here, using a real-space phase field model based on Ginzburg-Landau theory, we demonstrate that ferroelectric polarization can stabilize magnetic skyrmions at zero magnetic field in multiferroic heterostructures composed of MnSi, PbTiO3, and SrTiO3. The stabilization of magnetic skyrmions in multiferroic heterostructures essentially depends on the directions of spontaneous polarizations and the size ratios of different constituents, in which polarization-induced inhomogeneous strain plays an important role. By applying an electric field, the polarization switching takes place in the ferroelectric constituent and the polarization-induced strain changes in the multiferroic heterostructures, resulting in a transition from skyrmion to helical phase in the ferromagnetic constituent. In addition, the skyrmion and helical phases can coexist in the absence of an external field and be switched reversibly by a local magnetic field with a small magnitude. Stabilization and control of magnetic skyrmions by spontaneous polarization at zero magnetic field may create additional opportunities for nonvolatile skyrmion memory devices.