Over 600 people have been arrested while business leaders estimate that some 1,000 shops and companies have been looted
Five officers and eight civilians were hurt and taken to hospitals after the violence in the central town of Ixmiquilpan, but authorities did not specify whether the injuries were the result of gunshot wounds, or say who had fired.
The clash came on the fifth day of nationwide demonstrations and highway blockades that began when the government hiked gasoline prices by 20.1 percent on January 1.
More than 600 people have been arrested while business leaders estimate that some 1,000 shops and companies have been looted or vandalized this week as others closed over fears of being robbed.
The protests claimed the life of a police officer in Mexico City who died on Wednesday when he was struck by a car while preventing a theft at a service station.
In Ixmiquilpan, the Hidalgo state authorities said federal police tried to negotiate the peaceful removal of a roadblock on Thursday but protesters threw firecrackers and rocks at the officers.
"To deter the disturbances, the officers used tear gas, but the protesters did not withdraw and continued their aggressions, (and) gunfire was heard at the scene," the state public security department said in a statement.
President Enrique Pena Nieto used a nationally televised New Year's address late Thursday to defend the increase again.
"It is a difficult change but as president it is precisely my responsibility to take difficult decisions in the present to avoid major problems in the future," said Pena Nieto, whose approval rating has fallen below 25 percent in recent months.
He said the government could not maintain "artificial" prices as the international price of oil rose last year.
Keeping the same prices would have cost the government $9.3 billion, forcing the suspension of health care and welfare programs, he said.
"I ask you, what would you have done?"
Pena Nieto enacted a sweeping energy reform in 2014 that ended the monopoly held by state firm Pemex, inviting private firms to drill for oil as well as own service stations for the first time in decades.
The hike was imposed as the government prepares to stop fuel subsidies and let the market dictate gasoline prices from March.
But the steep increase shocked Mexicans in a country where nearly half the population lives in poverty.
Thousands of people marched in the northern industrial city of Monterrey, where a small group of masked demonstrators launched fireworks at the Nuevo Leon state government building and broke three windows.
Some 100 people marched peacefully in Mexico City.
"I have grandchildren and I would be ashamed to know that I did nothing" against the price increase, said Emma Cabrera Albarran, a 58-year-old shopkeeper at the Mexico City protest.
The national confederation of chambers of commerce, CONCANACO, estimated that between 700 and 800 small and medium-sized companies had been vandalized nationwide.
Separately, the National Association of Self-Service and Department Stores reported looting at nearly 250 shops in the capital and six other states.
"It's out of control," association executive Manuel Cardona told Radio Formula. He called on federal forces to intervene.
Dozens of people stormed a supermarket in the central city of Puebla, leaving with televisions, toys and king cake, which is eaten during the Catholic feast of the Epiphany, which falls this year on Friday.