A theory is developed of the time-dependent magnetization of the metacrystal composed of magnetoferritin macromolecules. Such superstructures, comprising up to several million superparamagnetic nanoparticles encapsulated in protein shells, can be created artificially using biochemical assembling technologies. They have been also shown to occur naturally in sensitive cells of the inner ear of birds, which suggests their possible involvement in the detection of the geomagnetic field for orientation and navigation of migratory animals. The dynamics of the magnetic system of the magnetoferritin metacrystal, comprising a very large number of magnetic moments coupled by long-range dipole forces, is exceedingly complex. In order to find the response of the metacrystal to high-frequency magnetic fields, we used a thermodynamic approach borrowed from the theory of nuclear spin systems of solids. The resulting theory yields the time-dependent superspin temperature and magnetization induced by oscillating magnetic fields of arbitrary strength. The predicted dependence of the high-frequency response on the static magnetic field can be used for experimental detection and characterization of magnetoferritin metacrystals in biological tissues.