The blast hit a facility owned by Mexico's state oil company, Pemex, in the port city of Coatzacoalcos.
Hundreds of people have been evacuated and schools closed. Footage showed a large fire and vast plumes of smoke.
The cause of the blast is unclear. Several explosions have been reported at Pemex facilities in recent years.
In pictures: Mexico explosion
The latest incident occurred at around 15:15 local time (20:15 GMT), Pemex said in a statement. Veracruz state Governor Javier Duarte told a radio station the blast was felt 10km (six miles) away.
The fire was under control by early evening, Pemex said. Residents were told to stay indoors because of the possible toxic nature of the smoke from the blast, but Pemex said the smoke dissipated quickly, lessening any possible toxic effects.
Of the 136 people injured, 88 remain in hospital, 13 of whom are in a serious condition, Pemex said.
Video posted on social media purporting to show a local hospital showed scenes of chaos and patients suffering heavy blood loss.
Pemex said the part of the factory hit by the explosion was managed by a sister company, Mexichem.
Associated Press reported that the plant produces vinyl chloride, a dangerous chemical used to make PVC pipes and packaging materials.
Exports of oil from the plant, one of the largest terminals for oil distribution in Mexico, would not be affected, the company added.
In September 2012, an explosion then a fire at a gas plant in the northern state of Tamaulipas killed 33 people.
Pemex's own headquarters in Mexico City was hit by a large gas blast in January 2013, killing 37 people.
A number of fires also struck the company's rigs in the Gulf of Mexico last year, and a worker was killed in another fire at the Veracruz plant in February this year.
A large explosion at an oil facility in the south-east Mexican state of Veracruz has killed at least three people and injured 136 more.