Medicare Better Health Rewards Program Act of 2013 - Amends title XVIII (Medicare) of the Social Security Act to direct the Secretary of Health and Human Services (HHS) to establish a three-year Better Health Rewards Program under which incentives are provided to Medicare beneficiaries who voluntarily agree to participate in the Program. Directs the Secretary to establish standards for measuring better health targets and points for achieving them for participating Medicare beneficiaries, including those for: (1) an annual wellness visit, (2) tobacco cessation, (3) Body Mass Index (BMI), (4) a diabetes screening test, (5) cardiovascular disease screening, (6) cholesterol level screening, and (7) screening tests and specified vaccinations. Requires the Secretary to make specified incentive payments to each participating Medicare beneficiary who achieves at least 20 points during a year. Authorizes Medicare Advantage Plans, "Section 1876" health maintenance organization and competitive medical cost plans, and programs of all-inclusive care for the elderly (PACE) to make incentives to their enrollees to participate in a Better Health Rewards Program. Amends the Internal Revenue Code to exclude from gross income any payment made under: (1) the Medicare Better Health Rewards Program, and (2) any other Better Health Rewards Program.