The massacre in the city of Uruapan in the western Michoacán state is thought to be gang-related, prosecutors say.
A banner hanging from the bridge reportedly bore the initials of one of Mexico's most powerful drug cartels.
Criminals have previously hung the bodies of their murdered victims in public to intimidate rival gangs.
"There is a turf war between the [local] cells of different criminal groups," state prosecutor Adrian López told reporters at a news conference on Thursday.
Mr López said the gangs, which he did not name, are "fighting for territorial control over the production, distribution and consumption of drugs".
Mexico still deadly turf for journalists
Mexican women who look for the dead
Mexico's López Obrador pledges 'radical' change
The banner on the bridge bore the initials of the Jalisco New Generation gang and a reference to a rival cartel, the Viagras, the Associated Press has reported.
Images on social media appeared to show the banner alongside numerous mutilated bodies.
The bodies were found in three locations across the city, where rival gangs are said to be battling for control of the drug trade.
Since 2006, when the Mexican government launched its war on drugs, Uruapan has been a hotbed of gang warfare and clashes between police and cartels.
As violence has escalated, so too has the murder rate. Last year, a record 33,341 murder investigations were opened by Mexican authorities, Reuters news agency reports.
Mexico's President Andrés Manuel López Obrador has tasked a new security force, the National Guard, with fighting the cartels.
But he has yet to make an impact is on Mexico's soaring murder rate. Mexico saw a 9.6% increase in murders in the first three months of 2019, official figures showed.