Three bodies were found in streets nearby.
A threatening message was left next to boxes, warning what were described as "traitors" and "blackmailers".
Guerrero state, home to the seaside resort of Acapulco, has been plagued by years of drug-related violence.
The latest gruesome incident created havoc around Chilpancingo.
The body parts were discovered at around 03:00 local time (08:00 GMT) on Sunday morning.
Police have not yet identified the victims. The gang has identified itself as Los Jefes, or The Bosses.
Some of Mexico's most notorious gangs have been fighting for control of drug routes along the country's Pacific coast.
Smaller criminal groups are also known to operate in Guerrero state, kidnapping for ransom and extorting farmers and shop owners.
In 2014, 43 students disappeared in Guerrero, in a high-profile case that highlighted the involvement of local authorities and police with organised crime.
Tens of thousands of people have died in drug-related violence in Mexico in the past decade.
A criminal gang in Mexico has dropped three iceboxes with a severed head in each one near a government building in Chilpancingo, the capital of the western state of Guerrero.