The FCC does regulate induction heaters. The regulations mainly are concerned with interference with other users in the frequency spectrum.
The main intent of an induction heater is to produce a magnetic field, not an electomagnetic field (radio wave). Propagation of magnetic field and electromagnetic fields are a little different, and I will leave that discussion for another time. So ideally, the electromagnetic part is contained within the enclosure of the induction heater's enclosure, while the magnetic field portion is, of course, outside of the enclosure (the heating coil which produces the magnetic field).
The means of creating the magnetic field (switching power supply) can of course create undesired electomagnetic emissions. This is where manufacturers have to work more diligently to not cause interference.
The FCC has allotted frequency bands exclusively for industrial heating use.
See this page for lots of boring details on industrial heaters.
The main enforcement for induction heaters is through complaints by other people using the frequency spectrum. At one time, a 200 KW 10 kHz induction heater, because of a poor installation, was effecting listeners of an AM radio station (1400 kHz) in St. Louis. Listeners complained, induction was located by FCC, problems corrected, every body happy then.