A direct search has been made for magnetic monopoles produced in e + p collisions at a centre of mass energy of 300 GeV at HERA. The beam pipe surrounding the interaction region in 1995-1997 was investigated using a SQUID magnetometer to look for stopped magnetic monopoles. During this time an integrated luminosity of 62 pb-1 was delivered. No magnetic monopoles were observed and charge and mass dependent upper limits on the e + p production cross section are set.