From the OED, I see that Hindi हिजड़ा hijaṛā "eunuch, impotent man" is perhaps borrowed (via Marathi हिजडा hijaḍā and Oriya ହିଜଡ଼ hijaṛa) from Kannada ಹೆಣ್ಣಿಗ heṇṇiga "impotent man, coward", ultimately from Tamil பெண்டன் peṇṭaṉ "hermaphrodite, eunuch". This is the masculine form of பெண்டு peṇṭu "woman".
Wikipedia notes (there is no citation) that Kannada initial h- is a reflex of earlier p-. It seems likely that the Kannada and Tamil words are both derived from the same proto-form.
No relation to Arabic هِجْرَة hijra, the migration of Muhammed to Medina.
Hijras are men who sacrifice their genitalia to a goddess in return for the power to confer fertility on newlyweds and newborn children, a ritual role they are respected for, at the same time as they are stigmatized for their ambiguous sexuality.
- Gayatri Reddy, With respect to sex: negotiating hijra identity in South India
Portraits of hijras.