Someone who's not able to speak suffers from mutism. Some types of mutism are caused by brain injury, while others have to do with the vocal cords.
You can also call mutism muteness. Both words stem from mute, which is rooted in the Latin mutus, "silent or speechless." Occasionally, mutism is the result of a person's conscious decision not to speak, but it can also be connected to trauma, delays in development, or a type of paralysis of the larynx, also known as the voice box.