IRS Abuse Protection Act of 2013 - Amends the Internal Revenue Code to require the Secretary of the Treasury to provide written notice to a taxpayer any time such taxpayer's account, tax return, or return information is accessed by the Department of the Treasury. Requires such notice to include: (1) who accessed such information, (2) the purpose for which such information was accessed, (3) how much information was accessed, (4) a copy of all information accessed, and (5) a notice of taxpayer rights. Prohibits the Secretary from providing access to or disclosing taxpayer information to a state entity conducting an investigation until such entity agrees to notify the Secretary, within one year after the investigation is closed, of the identity of who accessed such information, what was accessed, and why and how such information was accessed.

Requires the Inspector General for Tax Administration of the Department of the Treasury to notify a taxpayer of an investigation by the Inspector General of any unauthorized use of a taxpayer's account, tax return, or tax information and provide full access to any report with respect to such investigation.