Police told the BBC the victims, ages 15 to 25, were found in abandoned vehicles when they responded to a report of a fire at the Plaza Senderos shopping center.
Local media reports said three messages signed by Joaquin "El Chapo" Guzman, leader of the Sinaloa cartel and Mexico's most wanted drug lord, were found by the bodies.
The messages reportedly said the slayings were a warning to criminal groups fighting Guzman's syndicate. The drug trade in the Acapulco region is controlled by La Familia Michoacana.
It is believed to be the largest single group of decapitation victims found since President Felipe Calderon declared his offensive against the cartels four years ago. More than 30,000 people have been killed in drug-related violence in Mexico since then.
The BBC reported Acapulco has seen a sharp increase in drug-gang violence, even as the government insists it remains safe for tourists.