As Covid-19 vaccine mandates proliferate in the U.S. and Europe, so are swindlers selling bogus vaccination certificates.

The U.S. government has said federal workers must be vaccinated or submit to regular testing, mask requirements and social distancing. California requires state employees to be vaccinated or tested at least once a week. New York state will soon follow and New York City plans to require proof of vaccination for customers and staff at restaurants and gyms.

Employers such as Walt Disney Co. , Walmart Inc., Microsoft Corp. and Tyson Foods Inc. are requiring vaccination for at least some of their employees.

Proof of vaccination is required in parts of the U.S. and Europe to dine indoors, go to museums and attend large sporting events.

The spread of such rules has created a market for counterfeit certificates for the unvaccinated. In recent weeks, schemes to sell illegal proof of vaccination have multiplied on social-media sites, messaging apps such as Telegram and on the dark web, according to government investigators and cybersecurity experts.

“As a segment of the population tries to avoid the new measures, the dark net reacts to the real market and thus demand gives birth to offers,” said Dmitry Galov, a researcher at cybersecurity firm Kaspersky who has been tracking the sale of fake certificates since March.

In the U.S., fake vaccination cards purportedly issued by the Centers for Disease Control and Prevention have appeared for sale on sites such as AmazoneBay and Etsy. In May, officers arrested a bar owner in California for allegedly selling fake vaccination cards costing $20 each. The alleged perpetrator was charged with identity theft, forging government documents and falsifying medical records.

“While we do not have definitive numbers, we are seeing more of these types of schemes recently,” a Justice Department spokesman said.

The trade isn’t only online. Last month, the Justice Department arrested a licensed homeopathic doctor in California for allegedly selling patients what she called Covid immunization pellets. She then provided fake CDC vaccination cards that said the patients had received the Moderna vaccine. She also provided some patients with blank cards and instructions on how to complete them fraudulently by including a specific Moderna vaccine lot number.

In the U.S., the lack of a single federal digital card has made the work of swindlers easier. The small white cards issued by the CDC are easy to forge and weren’t intended to be a main source of proof of vaccination, according to security experts.

The European Union has a digital certificate with a dedicated QR code for each person. While the 27 member countries distribute their own vaccination cards, meaning there are variations in the format and where they are accepted, they use the same technology and there is a consensus on how they should be issued and used.

Despite the more-secure format, fake versions of the EU digital certificate have multiplied. In Italy, there are about 30 social-media profiles purporting to sell fake certificates, about 500 of which have been sold in the past few months, according to Ivano Gabrielli, an Italian police commander who oversees online fraud investigations. Telegram is the main platform being used for the sale of the fake certificates, he said.

“The sellers try to get the word out by posting vague information on well-known social-media platforms, but their goal is to get you to migrate over to an encrypted messaging app,” Mr. Gabrielli said.

A spokesman for Telegram said the company has shut down channels selling fake certificates when requested to do so by the Italian government.

When channels offering fake certificates do get shut down, new ones quickly appear with the same offers.