The Federal Aviation Administration is proposing a $350,000 fine on Amazon.com Inc. AMZN -1.79% for allegedly shipping prohibited dangerous goods by air.

The proposed fine stems from a 2014 incident in which nine United Parcel Service Inc. employees came into contact with a corrosive chemical that had leaked through a shipping package and had to be treated with a chemical wash after feeling a burning sensation. The liquid leaked from a one-gallon container of “Amazing Liquid Fire,” a drain cleaner, during a flight from Louisville, Ky. to Boulder, Colo.

The fine comes as the FAA is stepping up enforcement of hazardous materials safety violations and as Amazon is moving deeper into the world of shipping goods using its own network of airplanes, trucks and warehouses.

In 2015, the FAA handed out more than $4.5 million in civil penalties for improper shipments of hazardous materials aboard airplanes, up from $3.4 million in 2014, according to a report in the Dallas Morning News.

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The FAA has stepped up hazardous materials enforcement following several fires aboard aircraft. In 2010, a UPS Boeing 747 aircraft that had just taken off from Dubai International Airport crashed when a fire broke out in its cargo hold, which was carrying lithium batteries, killing both pilots.

Meanwhile, Amazon has moved further this year into the world of air freight, leasing 20 Boeing 767 aircraft from Air Transport Services Group Inc., its first major move towards building its own contract air freight fleet.

In the Amazon incident, the FAA alleged that the shipment was not properly packaged, was not accompanied by a proper declaration stating the hazardous nature of its contents, and that Amazon had failed to provide emergency response information with the package and that the Amazon employees who handled it had not received proper training.

“Amazon has a history of violating the Hazardous Materials Regulations,” the agency said in a news release. From February 2013 to September 2015, Amazon was found to have violated such regulations 24 times, the FAA said, adding that the agency would continue to investigate the company’s compliance with air safety regulations.

In the case that drew the civil penalty, the FAA said the e-commerce retailer didn’t label the shipment as carrying hazardous materials and had not trained workers in proper handling of such goods.

Kelly Cheeseman, a spokeswoman for Amazon, said in an emailed statement that the company takes air cargo safety “very seriously” and that Amazon has developed “sophisticated technologies to detect potential shipping hazards” in the tens of millions of shipments it sends every day.

Satish Jindel, founder of SJ Consulting Group Inc., which advises logistics companies, said Amazon will put stricter controls in place to address such lapses as the company develops more of its own shipping capabilities.

“As they try to do more of the distribution using their own network of air and ground services, knowing the distinction between what can go by ground and what can go by air will become more and more important,” Mr. Jindel said. “Before, when they were smaller, they didn’t have to make as many distinctions between ground and air.”

Write to Robbie Whelan at robbie.whelan@wsj.com