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.

The victim, 20, was found at a house in Crawley after paramedics were called about 03:00 BST.
He was found in Spencers Road, having sustained stab wound to the abdomen, and died a shortly afterwards in hospital.
Two men aged 24 and 22 and two 20-year-old men, all from Crawley, were detained and are in custody.
A police guard has been set up in Spencers Road and officers are speaking to residents in the area following the death of the man, who came from Mayfield.

Fellow Briton James DeGale, 29, who was the mandatory challenger, will now fight for the vacant title.
Froch, 37, wants to defend his WBA super-middleweight title this summer.
Talks have taken place over a potential bout against Mexico's Julio Cesar Chavez Junior in Las Vegas, or two-weight world champion Bernard Hopkins, 50, in Froch's home city of Nottingham.
Froch told BBC Radio 5 live a fight in Vegas or at Nottingham Forest's City Ground would be motivation to continue his career, although he has not ruled out retirement.
"Something needs to happen soon because if it doesn't, I will be retiring," added the boxer, who has won 33 of his 35 fights.
The four-time world champion said he felt frustrated at having to pull out of a fight with Chavez which was originally scheduled for March.
"I know what it's like to wait for a shot and I didn't want to hold James up in fighting for a world title," he said.
"James is a great fighter and I hope he can go out and win that title. Who knows... we may even meet later in the year."
DeGale earned the right to face Froch after beating Brandon Gonzalez on the undercard of Froch's Wembley fight against George Groves in May 2014.
Promoter Eddie Hearn is in negotiations for Degale to fight American Andre Dirrell for the IBF title and hopes the clash can take place on 25 April at London's O2 Arena.
"I'm making history," said DeGale. "I'm going to be the first British Olympic gold medallist to win a world title."
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.
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Four people have been arrested on suspicion of murder after a man was found with serious injuries.
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Carl Froch has vacated his IBF super-middleweight belt as he recovers from an elbow injury.