Primordial black holes (PBHs) with a mass M≲10^{17} g are expected to inject sub-GeV electrons and positrons in the Galaxy via Hawking radiation. These cosmic rays are shielded by the solar magnetic field for Earth-bound detectors, but not for Voyager 1, which is now beyond the heliopause. We use its data to constrain the fraction of PBHs to the dark matter in the Galaxy, finding that PBHs with M<10^{16} g cannot contribute more than 0.1% (or less for a log-normal mass distribution). Our limits are based on local Galactic measurements and are thus complementary to those derived from cosmological observations.