Manufacturing Reinvestment Account Act of 2013 - Amends the Internal Revenue Code to establish tax-exempt manufacturing reinvestment accounts (MRAs) for taxpayers engaged in a manufacturing business. Allows such manufacturers to make tax deductible cash payments into an MRA of the lesser of their domestic manufacturing gross receipts for the taxable year or $500,000. Permits expenditures from an MRA for expenses for property to be used in the manufacturing business and expenses for employee job training and workforce development. Imposes a 10% tax on amounts in an MRA that are not distributed within 7 years. Terminates the tax deduction for payments to an MRA 10 years after the enactment of this Act.