There's no legal minimum size a tire must be for it to be allowed for use at highway speeds. The size, weight and type of vehicle determine the appropriateness of a tire for highway use.
The smallest stock rim size put on automobiles are 13-inch rims matched to subcompact models. Some of these are as narrow as 145 mm.
The size of tires on street-legal motorcycles depends on the size of the motorcycle with smaller machines having smaller tires. The smallest is a 100 mm wide tire on a 16-inch rim. Tires smaller than this are found on mopeds and scooters but these won't achieve the speed limits set for the open road.
The tires on small utility trailers designed for highway use may fit rims as small as 8 inches. People who use their utility trailers on the road frequently upgrade to larger size wheels.