Electrically charged particles can be created by the decay of strong enough electric fields, a phenomenon known as the Schwinger mechanism1. By electromagnetic duality, a sufficiently strong magnetic field would similarly produce magnetic monopoles, if they exist2. Magnetic monopoles are hypothetical fundamental particles that are predicted by several theories beyond the standard model3-7 but have never been experimentally detected. Searching for the existence of magnetic monopoles via the Schwinger mechanism has not yet been attempted, but it is advantageous, owing to the possibility of calculating its rate through semi-classical techniques without perturbation theory, as well as that the production of the magnetic monopoles should be enhanced by their finite size8,9 and strong coupling to photons2,10. Here we present a search for magnetic monopole production by the Schwinger mechanism in Pb-Pb heavy ion collisions at the Large Hadron Collider, producing the strongest known magnetic fields in the current Universe11. It was conducted by the MoEDAL experiment, whose trapping detectors were exposed to 0.235 per nanobarn, or approximately 1.8 × 109, of Pb-Pb collisions with 5.02-teraelectronvolt center-of-mass energy per collision in November 2018. A superconducting quantum interference device (SQUID) magnetometer scanned the trapping detectors of MoEDAL for the presence of magnetic charge, which would induce a persistent current in the SQUID. Magnetic monopoles with integer Dirac charges of 1, 2 and 3 and masses up to 75 gigaelectronvolts per speed of light squared were excluded by the analysis at the 95% confidence level. This provides a lower mass limit for finite-size magnetic monopoles from a collider search and greatly extends previous mass bounds.