Hello, I'm Alicia. Thanks for your question, I'm happy to help you today.
There are several mental health - or psychiatric - disorders that fit into the "non-empathetic" category, meaning that people with these diagnoses have an inability to show empathy or concern for others. Personality disorders like Narcissistic Personality Disorder, Borderline Personality Disorder
and Anti-social Personality Disorder (see here for more information: http://www.psychologytoday.com/blog/stop-walking-eggshells/201201/lack-empathy-the-most-telling-narcissistic-trait) are the main disorders that would match this criteria. People with Bipolar
Disorder (a mood, not personality disorder) also often demonstrate an inability to display empathy, especially during a manic phase. See here: http://www.bipolarcentral.com/documents/Bipolar-Disorder-Symptoms/Narcissism-vs-Bipolar-Disorder.php
Unfortunately, while possible, treatment for people with these disorders is sometimes difficult and not always successful.
You might also find this article interesting:
I hope that helps, please let me know if you have any further questions. Best wishes.