DEFINITION of 'Sherman Antitrust Act'. Anti-monopoly U.S. legislation which attempted to increase economic competitiveness. The Sherman Antitrust Act of 1890 made it illegal for companies to seek a monopoly on a product or service, or form cartels.Next Up.he Sherman Antitrust Act of 1890 made it illegal for companies to seek a monopoly on a product or service, or form cartels.