Superparamagnetic iron nanoparticles with a size of a few nanometers were produced in copper by severe plastic deformation. In a isochronal annealing experiment near a temperature of 450 K, which corresponds to the temperature of structural relaxation and the first step of grain growth (from 128 to 150 nm) of submicrocrystalline copper, an abrupt increase in the magnetic susceptibility is detected. This increase is shown to be due to iron nanoparticles increasing in size from 2.8 to 3.3 nm. The vanishing of the ferromagnetic contribution by iron nanoparticles observed at 850 K, well below the Curie temperature of iron, is due to the dissolution of nanoparticles in plastically deformed copper.