The availability of accessible fabrication methods based on deterministic transfer of atomically thin crystals has been essential for the rapid expansion of research into van der Waals heterostructures. An inherent issue of these techniques is the deformation of the polymer carrier film during the transfer, which can lead to highly non-uniform strain induced in the transferred two-dimensional material. Here, using a combination of optical spectroscopy, atomic force and Kelvin probe force microscopy, we show that the presence of nanometer scale wrinkles formed due to transfer-induced stress relaxation can lead to strong changes in the optical properties of MoSe$_2$/WSe$_2$ heterostructures and the emergence of the linearly polarized interlayer exciton photoluminescence. We attribute these changes to the local breaking of crystal symmetry in the nanowrinkles, which act as efficient accumulation centers for the interlayer excitons due to the strain-induced interlayer band gap reduction. The surface potential images of the rippled heterobilayer samples acquired using Kelvin probe force microscopy reveal the variation of the local work function consistent with the strain-induced band gap modulation, while the potential offset observed at the ridges of the wrinkles shows a clear correlation with the value of the tensile strain estimated from the wrinkle geometry. Our findings highlight the important role of the residual strain in defining optical properties of van der Waals heterostructures and suggest novel approaches for interlayer exciton manipulation by local strain engineering.