DSH Reduction Relief Act of 2013 - Amends title XVIII (Medicare) of the Social Security Act (SSA) to delay from FY2014 to FY2016 commencement of the period during which the Secretary of Health and Human Services (HHS) is required to pay to any "subsection (d) hospital": (1) 25% of the amount of the disproportionate share hospital (DSH) payment that would otherwise be made to it for the fiscal year, plus (2) an additional payment amount according to a specified formula.

(Generally, a subsection [d] hospital is an acute care hospital, particularly one that receives payments under Medicare's inpatient prospective payment system [IPPS] when providing covered inpatient services to eligible beneficiaries.)

Amends SSA title XIX (Medicaid) to delay from the beginning of FY2014 until the beginning of FY2016 (and so eliminate for FY2014 and FY2015) aggregate reductions in DSH allotments for all states.

Maintains the FY2022 DSH allotment to states under Medicaid for FY2023, with an adjustment for inflation.