Fair Minimum Wage Act of 2013 - Amends the Fair Labor Standards Act of 1938 (FLSA) to increase the federal minimum wage for employees to: (1) $8.50 an hour on the first day of the third month after enactment of this Act; (2) $10.00 an hour after one year; (3) $11.00 an hour after two years; and (4) the amount determined by the Secretary of Labor (based on increases in the Consumer Price Index) after three years, and annually thereafter.

Increases the federal minimum wage for tipped employees to $3.00 an hour for one year on the first day of the third month after enactment of this Act. Provides a formula for subsequent annual adjustments of the wage increase to ensure that it remains equal to 70% of the wage in effect under FLSA for other employees.

Directs the Secretary, 60 days before any increase in the minimum wage, to publish it in the Federal Register and on the Department of Labor's website.