If a heavy neutrino of mass 1.1 MeV <m <14 MeV participates in the weak charged current coupling for the electron, then it can be produced in the Sun and decay in flight into an electron, a positron and a light neutrino. It is shown here that existing experimental bounds on low-energy interplanetary positrons severely constrain the heavy neutrino-electron coupling. Accelerator experiments severely constrain the coupling of still heavier neutrinos.