Abortion Non-Discrimination Act of 2013 - Amends the Public Health Service Act to codify the prohibition against any action by the federal government and any state or local government receiving federal financial assistance to subject a health professional, a hospital, a provider-sponsored organization, a health maintenance organization, an accountable care organization, a health insurance plan, or any other kind of health care facility, organization, or plan to discrimination on the basis that the entity refuses to participate in abortion-related activities.

Creates a cause of action for any violation of the abortion discrimination prohibition. Gives federal courts jurisdiction to prevent and redress actual or threatened violations of such prohibition by issuing any form of legal or equitable relief, including injunctions and orders preventing the disbursement of all or a portion of federal financial assistance until the prohibited conduct has ceased. Gives standing to institute an action to affected health care entities and the Attorney General.

Requires the Secretary of Health and Human Services to designate the Director of the Office for Civil Rights of the Department of Health and Human Services (HHS) to receive and investigate complaints alleging a violation of abortion discrimination prohibition.