No, being transgender is not a mental disorder; however, mental health assessment and care is often an integral part of transgender care.
Transgender people often seek therapy for help in exploring their gender identity, or for mental health conditions like depression, anxiety, or substance abuse that may be related to societal discrimination and trauma, which are commonly experienced by trans people.
In fact, according to the APA, most transgender people are likely to have mental disorders due to how they are treated by society or others.
Unlike a majority of mental disorders, being transgender is present within an individual from childhood. For starters, transgender people have a unique brain structure from cisgender people. Their brain function resembles that of the gender they embrace on the inside. These differences in brain structure exist in all transgender people regardless of whether they have started hormone treatment.