Do doctors consider extreme shyness as a mental illness?

No: Shyness is not a psychiatric diagnosis, though some disorders can present as or lead to shyness, especially anxiety disorders. An informal term of "pathological shyness" refers to someone so shy in so many situations and to such an extent that it impairs function; often, such people have a fairly severe anxiety disorder or other condition that, if treated, would make the shyness less severe.