Magnetic monopoles have long been predicted in theory and could exist as a stable object in our Universe. As they move around in galaxies, magnetic monopoles could be captured by astrophysical objects like stars and planets. Here, we provide a novel method to search for magnetic monopoles by detecting the monopole moment of Earth's magnetic field. Using over six years of public geomagnetic field data obtained by the Swarm satellites, we apply Gauss's law to measure the total magnetic flux, which is proportional to the total magnetic charge inside Earth. To account for the secular variation of satellite altitudes, we define an altitude-rescaled magnetic flux to reduce the dominant magnetic dipole contribution. The measured magnetic flux is consistent with the existing magnetic field model that does not contain a monopole moment term. We therefore set an upper limit on the magnetic field strength at Earth's surface from magnetic monopoles to be |Bm|<0.13 nT at 95% confidence level, which is less than 2×10-6 of Earth's magnetic field strength. This constrains the abundance of magnetically charged objects, including magnetic black holes with large magnetic charges.