Yes. Commercial high-speed cameras do exist with extremely short exposure times, including sub-microsecond ranges; one community answer specifically mentions Photron models reaching into the 100-nanosecond range. The main limitation is not availability in principle, but cost: these systems are typically very expensive, often in the tens-of-thousands-of-dollars class, so renting may be possible through specialty providers but ownership is usually unrealistic for hobby use.

The other big challenge is light. At sub-microsecond exposure times, you need a very intense light source or a different approach such as ultra-short flash illumination, because ordinary continuous lighting usually won’t be enough.

So the short answer is: yes, such cameras exist, but they are specialist tools, expensive, and difficult to light properly. If your goal is mainly to freeze the motion rather than record long sequences, alternative methods may be more practical depending on exactly what you want to measure or visualize.