Anheuser-Busch InBev NV is attempting to forge a global brewing juggernaut by acquiring chief rival SABMiller PLC, but a proposed tie-up would face intense antitrust scrutiny and send shock waves far beyond beer.

Regulators likely would press for major concessions from AB InBev, particularly in the U.S. and China, to put the brakes on two brewers that together already produce nearly a third of the world’s beer and span hundreds of brands including Budweiser, Corona and Peroni. AB InBev and SABMiller had 20.8% and 9.7% world-wide...