No known astrophysical mechanisms are expected to generate a significant high-energy flux of cosmic-ray electrons and positrons (CREs) from the Sun. However, some recently considered classes of dark matter models predict such a signal. We analyzed the CRE events collected by the Fermi-LAT during its first year of operation to search for a flux excess correlated with the Sun's direction, and found no evidence of a significant signal. I will discuss the constraints these results place on secluded dark matter models and inelastic dark matter models.